http://wiki.math.bme.hu/history/Matematika_k%C3%B6zlek_a3_2010_4._gyakorlat?feed=atom&
Matematika közlek a3 2010 4. gyakorlat - Laptörténet
2024-03-29T04:44:41Z
Az oldal laptörténete a wikiben
MediaWiki 1.18.1
http://wiki.math.bme.hu/index.php?title=Matematika_k%C3%B6zlek_a3_2010_4._gyakorlat&diff=6368&oldid=prev
Mozo: /* Komplex elemi függvények */
2010-09-27T19:20:26Z
<p><span class="autocomment">Komplex elemi függvények</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2010. szeptember 27., 19:20-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">12. sor:</td>
<td colspan="2" class="diff-lineno">12. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}=\frac{e^{3i+4}-e^{-3i-4}}{2i}=\frac{e^{3i}e^4-e^{-3i}}{2i}=...</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}=\frac{e^{3i+4}-e^{-3i-4}}{2i}=\frac{e^{3i}e^4-e^{-3i}}{2i}=...</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\mathrm{ln}(-5+5i)=\mathrm{ln}(5\sqrt{2})+\mathrm{ln}(\frac{3}{4}\pi i)=\mathrm{ln}(5\sqrt{2})+i\frac{3}{4}\pi</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\mathrm{ln}(-5+5i)=\mathrm{ln}(5\sqrt{2})+\mathrm{ln}(\frac{3}{4}\pi i)=\mathrm{ln}(5\sqrt{2})+i\frac{3}{4}\pi</math></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Oldjuk meg!</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"># <math>e^{-z}+1=0\,</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"># <math>\sin(z i)=0\,</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"># <math>\sin 5^z=1\,</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">''Mo.''</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">:<math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">e^{-z\pi}=-1=e^{\pi i}\,</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">:<math>-z\pi=\pi i +2k\pi i\,</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">:<math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">e^{-z}-\frac{1}{e^{z}}=0\,</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">...</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">:<math>e^{5^z}-\frac{1}{e^{5^{z}}}=1\,</math></ins></div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_k%C3%B6zlek_a3_2010_4._gyakorlat&diff=6367&oldid=prev
Mozo: /* Komplex elemi függvények */
2010-09-27T18:32:10Z
<p><span class="autocomment">Komplex elemi függvények</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2010. szeptember 27., 18:32-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">11. sor:</td>
<td colspan="2" class="diff-lineno">11. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}=\frac{e^{3i+4}-e^{-3i-4}}{2i}=\frac{e^{3i}e^4-e^{-3i}}{2i}=...</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}=\frac{e^{3i+4}-e^{-3i-4}}{2i}=\frac{e^{3i}e^4-e^{-3i}}{2i}=...</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<math>\mathrm{ln}(-5+5i)=\mathrm{ln}(5\sqrt{2})+\mathrm{ln}(\frac{3}{4}\pi i)=\mathrm{ln}(5\sqrt{2})+i\frac{3}{4}\pi<del class="diffchange diffchange-inline">=</del></math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<math>\mathrm{ln}(-5+5i)=\mathrm{ln}(5\sqrt{2})+\mathrm{ln}(\frac{3}{4}\pi i)=\mathrm{ln}(5\sqrt{2})+i\frac{3}{4}\pi</math></div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_k%C3%B6zlek_a3_2010_4._gyakorlat&diff=6366&oldid=prev
Mozo: /* Komplex elemi függvények */
2010-09-27T18:31:49Z
<p><span class="autocomment">Komplex elemi függvények</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2010. szeptember 27., 18:31-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">11. sor:</td>
<td colspan="2" class="diff-lineno">11. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}=\frac{e^{3i+4}-e^{-3i-4}}{2i}=\frac{e^{3i}e^4-e^{-3i}}{2i}=...</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}=\frac{e^{3i+4}-e^{-3i-4}}{2i}=\frac{e^{3i}e^4-e^{-3i}}{2i}=...</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<math>\mathrm{ln}(-5+5i)=\mathrm{ln}(5\sqrt{2})+\mathrm{ln}(<del class="diffchange diffchange-inline">5i</del>)=\mathrm{ln}(5\sqrt{2})+i\frac{3}{4}\pi=</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<math>\mathrm{ln}(-5+5i)=\mathrm{ln}(5\sqrt{2})+\mathrm{ln}(<ins class="diffchange diffchange-inline">\frac{3}{4}\pi i</ins>)=\mathrm{ln}(5\sqrt{2})+i\frac{3}{4}\pi=</math></div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_k%C3%B6zlek_a3_2010_4._gyakorlat&diff=6365&oldid=prev
Mozo: /* Komplex elemi függvények */
2010-09-27T18:30:57Z
<p><span class="autocomment">Komplex elemi függvények</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2010. szeptember 27., 18:30-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">11. sor:</td>
<td colspan="2" class="diff-lineno">11. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}=\frac{e^{3i+4}-e^{-3i-4}}{2i}=\frac{e^{3i}e^4-e^{-3i}}{2i}=...</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}=\frac{e^{3i+4}-e^{-3i-4}}{2i}=\frac{e^{3i}e^4-e^{-3i}}{2i}=...</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<math>\mathrm{ln}(-5+5i)=\mathrm{ln}(5\sqrt{2})5i)</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<math>\mathrm{ln}(-5+5i)=\mathrm{ln}(5\sqrt{2})<ins class="diffchange diffchange-inline">+\mathrm{ln}(</ins>5i)<ins class="diffchange diffchange-inline">=\mathrm{ln}(5\sqrt{2})+i\frac{3}{4}\pi=</ins></math></div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_k%C3%B6zlek_a3_2010_4._gyakorlat&diff=6364&oldid=prev
Mozo: /* Komplex elemi függvények */
2010-09-27T18:27:47Z
<p><span class="autocomment">Komplex elemi függvények</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2010. szeptember 27., 18:27-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">10. sor:</td>
<td colspan="2" class="diff-lineno">10. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}<ins class="diffchange diffchange-inline">=\frac{e^{3i+4}-e^{-3i-4}}{2i}=\frac{e^{3i}e^4-e^{-3i}}{2i}=...</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:<math>\mathrm{ln}(-5+5i)=\mathrm{ln}(5\sqrt{2})5i)</ins></math></div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_k%C3%B6zlek_a3_2010_4._gyakorlat&diff=6363&oldid=prev
Mozo: /* Komplex elemi függvények */
2010-09-27T17:08:49Z
<p><span class="autocomment">Komplex elemi függvények</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2010. szeptember 27., 17:08-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">6. sor:</td>
<td colspan="2" class="diff-lineno">6. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>\mathrm{sh}(1+i\frac{\pi}{2})</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>\mathrm{sh}(1+i\frac{\pi}{2})</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>e^{1-i\,\mathrm{arc\,sin}\,\frac{1}{3}}</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>e^{1-i\,\mathrm{arc\,sin}\,\frac{1}{3}}</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div># <math>\mathrm{ln}(-5+5i)</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div># <math>\mathrm{ln}(-5+5i)<ins class="diffchange diffchange-inline">\,</ins></math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div># <math>(1+i)^{i}</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div># <math>(1+i)^{i}<ins class="diffchange diffchange-inline">\,</ins></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}</math></div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_k%C3%B6zlek_a3_2010_4._gyakorlat&diff=6362&oldid=prev
Mozo: /* Komplex elemi függvények */
2010-09-27T17:08:30Z
<p><span class="autocomment">Komplex elemi függvények</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2010. szeptember 27., 17:08-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">5. sor:</td>
<td colspan="2" class="diff-lineno">5. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>\sin(3-4i)\,</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>\sin(3-4i)\,</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>\mathrm{sh}(1+i\frac{\pi}{2})</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>\mathrm{sh}(1+i\frac{\pi}{2})</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div># <math>e^{1-i\mathrm{arc\,sin}\,\frac{1}{3}}</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div># <math>e^{1-i<ins class="diffchange diffchange-inline">\,</ins>\mathrm{arc\,sin}\,\frac{1}{3}}</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>\mathrm{ln}(-5+5i)</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>\mathrm{ln}(-5+5i)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>(1+i)^{i}</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>(1+i)^{i}</math></div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_k%C3%B6zlek_a3_2010_4._gyakorlat&diff=6361&oldid=prev
Mozo: /* Komplex elemi függvények */
2010-09-27T17:08:05Z
<p><span class="autocomment">Komplex elemi függvények</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2010. szeptember 27., 17:08-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">3. sor:</td>
<td colspan="2" class="diff-lineno">3. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Adjuk meg algebrai alakban:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Adjuk meg algebrai alakban:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div># <math>\sin(3-4i)</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div># <math>\sin(3-4i)<ins class="diffchange diffchange-inline">\,</ins></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>\mathrm{sh}(1+i\frac{\pi}{2})</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>\mathrm{sh}(1+i\frac{\pi}{2})</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>e^{1-i\mathrm{arc\,sin}\,\frac{1}{3}}</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div># <math>e^{1-i\mathrm{arc\,sin}\,\frac{1}{3}}</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div># <math>\mathrm{ln}<del class="diffchange diffchange-inline">\,</del>-5+5i</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div># <math>\mathrm{ln}<ins class="diffchange diffchange-inline">(</ins>-5+5i<ins class="diffchange diffchange-inline">)</ins></math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div># (1+i)^{i}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div># <ins class="diffchange diffchange-inline"><math></ins>(1+i)^{i}<ins class="diffchange diffchange-inline"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">''Mo.'' </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:<math>\sin(3-4i)=\frac{e^{i(3-4i)}-e^{-i(3-4i)}}{2i}</math></ins></div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_k%C3%B6zlek_a3_2010_4._gyakorlat&diff=6360&oldid=prev
Mozo, 2010. szeptember 27., 17:05-n
2010-09-27T17:05:21Z
<p></p>
<p><b>Új lap</b></p><div>==Komplex elemi függvények==<br />
<br />
Adjuk meg algebrai alakban:<br />
<br />
# <math>\sin(3-4i)</math><br />
# <math>\mathrm{sh}(1+i\frac{\pi}{2})</math><br />
# <math>e^{1-i\mathrm{arc\,sin}\,\frac{1}{3}}</math><br />
# <math>\mathrm{ln}\,-5+5i</math><br />
# (1+i)^{i}</div>
Mozo