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Övningar 3.1 - Versionshistorik
2026-06-21T11:11:02Z
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http://wiki.math.se/wikis/sf0601_0701/index.php?title=%C3%96vningar_3.1&diff=1178&oldid=prev
KTH.SE:u1zpa8nw den 18 juli 2007 kl. 08.45
2007-07-18T08:45:58Z
<p></p>
<table border='0' width='98%' cellpadding='0' cellspacing='4' style="background-color: white;">
<tr>
<td colspan='2' width='50%' align='center' style="background-color: white;">← Äldre version</td>
<td colspan='2' width='50%' align='center' style="background-color: white;">Versionen från 18 juli 2007 kl. 08.45</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 1:</strong></td>
<td colspan="2" align="left"><strong>Rad 1:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">'''Övning 3.1:1'''</td><td> </td><td style="background: #eee; font-size: smaller;">'''Övning 3.1:1'''</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning">Skriv i formen $\,a+bi\,$, där $\,a\,$ och $\,b\,$ är reella tal</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">Skriv i formen $\,a+bi\,$, där $\,a\,$ och $\,b\,$ är reella tal</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><table width="100%" cellspacing="10px"></td><td> </td><td style="background: #eee; font-size: smaller;"><table width="100%" cellspacing="10px"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 43:</strong></td>
<td colspan="2" align="left"><strong>Rad 42:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">'''Övning 3.1:3'''</td><td> </td><td style="background: #eee; font-size: smaller;">'''Övning 3.1:3'''</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning">Bestäm det reella tal $\,a\,$ så att uttrycket $\ \displaystyle\frac{3+i}{2+ai}\ $ blir rent imaginärt (dvs. realdel lika med noll). </td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">Bestäm det reella tal $\,a\,$ så att uttrycket $\ \displaystyle\frac{3+i}{2+ai}\ $ blir rent imaginärt (dvs. realdel lika med noll). </td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">'''Övning 3.1:4'''</td><td> </td><td style="background: #eee; font-size: smaller;">'''Övning 3.1:4'''</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning">Lös ekvationerna</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">Lös ekvationerna</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><table width="100%" cellspacing="10px"></td><td> </td><td style="background: #eee; font-size: smaller;"><table width="100%" cellspacing="10px"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0601_0701/index.php?title=%C3%96vningar_3.1&diff=1177&oldid=prev
KTH.SE:u1zpa8nw den 18 juli 2007 kl. 08.44
2007-07-18T08:44:58Z
<p></p>
<table border='0' width='98%' cellpadding='0' cellspacing='4' style="background-color: white;">
<tr>
<td colspan='2' width='50%' align='center' style="background-color: white;">← Äldre version</td>
<td colspan='2' width='50%' align='center' style="background-color: white;">Versionen från 18 juli 2007 kl. 08.44</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 71:</strong></td>
<td colspan="2" align="left"><strong>Rad 71:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></table></td><td> </td><td style="background: #eee; font-size: smaller;"></table></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br></td></tr>
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KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0601_0701/index.php?title=%C3%96vningar_3.1&diff=1176&oldid=prev
KTH.SE:u1zpa8nw: Ny sida: '''Övning 3.1:1''' <div class="ovning"> Skriv i formen $\,a+bi\,$, där $\,a\,$ och $\,b\,$ är reella tal <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</t...
2007-07-18T08:44:31Z
<p>Ny sida: '''Övning 3.1:1''' <div class="ovning"> Skriv i formen $\,a+bi\,$, där $\,a\,$ och $\,b\,$ är reella tal <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</t...</p>
<p><b>Ny sida</b></p><div>'''Övning 3.1:1'''<br />
<div class="ovning"><br />
Skriv i formen $\,a+bi\,$, där $\,a\,$ och $\,b\,$ är reella tal<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$(5-2i)+(3+5i)$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$3i -(2-i)$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$ i(2+3i)$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$(3-2i)(7+5i)$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="50%">$ (1+i)(2-i)^2$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="50%">$i^{\,20} + i^{\,11}$</td><br />
</tr><br />
</table><br />
</div><br />
<br />
'''Övning 3.1:2'''<br />
<div class="ovning">Skriv i formen $\,a+ib\,$, där $\,a\,$ och $\,b\,$ är reella tal<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\displaystyle\frac{3-2i}{1+i}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\displaystyle\frac{3i}{4-6i} - \displaystyle\frac{1+i}{3+2i}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$ \displaystyle\frac{(2-i\sqrt{3}\,)^2}{1+i\sqrt{3}}$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$\displaystyle\frac{5-\displaystyle\frac{1}{1+i}}{3i + \displaystyle\frac{i}{2-3i}}$</td><br />
</tr><br />
</table><br />
</div><br />
<br />
'''Övning 3.1:3'''<br />
<div class="ovning"><br />
Bestäm det reella tal $\,a\,$ så att uttrycket $\ \displaystyle\frac{3+i}{2+ai}\ $ blir rent imaginärt (dvs. realdel lika med noll). <br />
</div><br />
<br />
'''Övning 3.1:4'''<br />
<div class="ovning"><br />
Lös ekvationerna<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$z+3i=2z-2$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$(2-i) z= 3+2i$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$ iz+2= 2z-3$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$(2+i) \overline{z} = 1+i$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="50%">$ \displaystyle\frac{iz+1}{z+i} = 3+i$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="50%">$(1+i)\overline{z}+iz = 3+5i$</td><br />
</tr><br />
</table><br />
</div></div>
KTH.SE:u1zpa8nw