KTH.SE:u1zpa8nw den 18 juli 2007 kl. 09.00

KTH.SE:u1zpa8nw — Wed, 18 Jul 2007 09:00:50 GMT

← Äldre version		Versionen från 18 juli 2007 kl. 09.00
Rad 59:		Rad 59:
	<td class="ntext" width="50%">$(3-4i)(3+2i)$</td>		<td class="ntext" width="50%">$(3-4i)(3+2i)$</td>
	<td class="ntext">d)</td>		<td class="ntext">d)</td>
-	<td class="ntext" width="50%">$\displaystyle\frac{3-4i}{3+2i}$</td>	+	<td class="ntext" width="50%">$\quad\displaystyle\frac{3-4i}{3+2i}$</td>
	</tr>		</tr>
	</table>		</table>
Rad 99:		Rad 99:
	<tr align="left">		<tr align="left">
	<td class="ntext">e)</td>		<td class="ntext">e)</td>
-	<td class="ntext" width="50%">$ \displaystyle\frac{1+i\sqrt{3}}{1+i}$</td>	+	<td class="ntext" width="50%">$\quad\displaystyle\frac{1+i\sqrt{3}}{1+i}$</td>
	<td class="ntext">f)</td>		<td class="ntext">f)</td>
-	<td class="ntext" width="50%">$\displaystyle\frac{(2+2i)(1+i\sqrt{3}\,)}{3i(\sqrt{12} -2i)}$</td>	+	<td class="ntext" width="50%">$\quad\displaystyle\frac{(2+2i)(1+i\sqrt{3}\,)}{3i(\sqrt{12} -2i)}$</td>
	</tr>		</tr>
	</table>		</table>
	</div>		</div>
	<br><br><br><br><br><br>		<br><br><br><br><br><br>

KTH.SE:u1zpa8nw: Ny sida: '''Övning 3.2:1'''
Givet de komplexa talen $\,z=2+i\,$, $\,w=2+3i\,$ och $\,u=-1-2i\,$. Markera följande tal i det kompl...

KTH.SE:u1zpa8nw — Wed, 18 Jul 2007 08:50:50 GMT

Ny sida: '''Övning 3.2:1''' <div class="ovning" style="margin-top:-20px; margin-bottom:-18px;">Givet de komplexa talen $\,z=2+i\,$, $\,w=2+3i\,$ och $\,u=-1-2i\,$. Markera följande tal i det kompl...

Ny sida

'''Övning 3.2:1'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-18px;">Givet de komplexa talen $\,z=2+i\,$, $\,w=2+3i\,$ och $\,u=-1-2i\,$. Markera följande tal i det komplexa talplanet
<table width="100%" cellspacing="10px">
<tr align="left">
<td class="ntext">a)</td>
<td class="ntext" width="50%">$z\,$ och $\,w$</td>
<td class="ntext">b)</td>
<td class="ntext" width="50%">$z+u\,$ och $\,z-u$</td>
</tr>
<tr align="left">
<td class="ntext">c)</td>
<td class="ntext" width="50%">$2z+w$</td>
<td class="ntext">d)</td>
<td class="ntext" width="50%">$z-\overline{w}+u$</td>
</tr>
</table>
</div>

'''Övning 3.2:2'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-18px;">Rita in följande mängder i det komplexa talplanet
<table width="100%" cellspacing="10px">
<tr align="left">
<td class="ntext">a)</td>
<td class="ntext" width="50%">$0\le \mbox{Im}\, z \le 3$</td>
<td class="ntext">b)</td>
<td class="ntext" width="50%">$0 \le \mbox{Re} \, z \le \mbox{Im}\, z \le 1$</td>
</tr>
<tr align="left">
<td class="ntext">c)</td>
<td class="ntext" width="50%">$ |z|=2$</td>
<td class="ntext">d)</td>
<td class="ntext" width="50%">$|z-1-i|=3$</td>
</tr>
<tr align="left">
<td class="ntext">e)</td>
<td class="ntext" width="50%">$ \mbox{Re}\, z = i + \bar z$</td>
<td class="ntext">f)</td>
<td class="ntext" width="50%">$2<|z-i|\le3$</td>
</tr>
</table>
</div>

'''Övning 3.2:3'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-18px;">De komplexa talen $\,1+i\,$, $\,3+2i\,$ och $\,3i\,$ bildar i det komplexa talplanet tre hörn i en kvadrat. Bestäm kvadratens fjärde hörn.
</div>

'''Övning 3.2:4'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-18px;">
Bestäm beloppet av
<table width="100%" cellspacing="10px">
<tr align="left">
<td class="ntext">a)</td>
<td class="ntext" width="50%">$3+4i$</td>
<td class="ntext">b)</td>
<td class="ntext" width="50%">$(2-i) + (5+3i)$</td>
</tr>
<tr align="left">
<td class="ntext">c)</td>
<td class="ntext" width="50%">$(3-4i)(3+2i)$</td>
<td class="ntext">d)</td>
<td class="ntext" width="50%">$\displaystyle\frac{3-4i}{3+2i}$</td>
</tr>
</table>
</div>

'''Övning 3.2:5'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-18px;">Bestäm argumentet av
<table width="100%" cellspacing="10px">
<tr align="left">
<td class="ntext">a)</td>
<td class="ntext" width="50%">$-10$</td>
<td class="ntext">b)</td>
<td class="ntext" width="50%">$-2+2i$</td>
</tr>
<tr align="left">
<td class="ntext">c)</td>
<td class="ntext" width="50%">$ (\sqrt{3} +i)(1-i)$</td>
<td class="ntext">d)</td>
<td class="ntext" width="50%">$\displaystyle\frac{i}{1+i}$</td>
</tr>
</table>
</div>

'''Övning 3.2:6'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-18px;">Skriv följande tal i polär form
<table width="100%" cellspacing="10px">
<tr align="left">
<td class="ntext">a)</td>
<td class="ntext" width="50%">$3$</td>
<td class="ntext">b)</td>
<td class="ntext" width="50%">$-11i$</td>
</tr>
<tr align="left">
<td class="ntext">c)</td>
<td class="ntext" width="50%">$ -4-4i$</td>
<td class="ntext">d)</td>
<td class="ntext" width="50%">$\sqrt{10} + \sqrt{30}\,i$</td>
</tr>
<tr align="left">
<td class="ntext">e)</td>
<td class="ntext" width="50%">$ \displaystyle\frac{1+i\sqrt{3}}{1+i}$</td>
<td class="ntext">f)</td>
<td class="ntext" width="50%">$\displaystyle\frac{(2+2i)(1+i\sqrt{3}\,)}{3i(\sqrt{12} -2i)}$</td>
</tr>
</table>
</div>
<br><br><br><br><br><br>

Övningar 3.2 - Versionshistorik

KTH.SE:u1zpa8nw den 18 juli 2007 kl. 09.00

KTH.SE:u1zpa8nw: Ny sida: '''Övning 3.2:1''' Givet de komplexa talen $\,z=2+i\,$, $\,w=2+3i\,$ och $\,u=-1-2i\,$. Markera följande tal i det kompl...

KTH.SE:u1zpa8nw: Ny sida: '''Övning 3.2:1'''
Givet de komplexa talen $\,z=2+i\,$, $\,w=2+3i\,$ och $\,u=-1-2i\,$. Markera följande tal i det kompl...