# putting complex numbers into form x+yj

• October 26th 2008, 07:34 AM
philyc86
putting complex numbers into form x+yj
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• October 26th 2008, 08:58 AM
shawsend
$\frac{z-1}{z}=-\frac{i}{1-i}=1/2(1+i);\quad z=1-i$

$\sqrt{1/2(1+i)}=\frac{1}{\sqrt{2}}\sqrt{1+i}$

$=\frac{1}{\sqrt{2}} 2^{1/4}e^{i/2(\Theta+2k\pi)}$

then:

$r_1=2^{-1/4}e^{\pi i/8}$

$r_2=2^{-1/4}e^{9\pi i/8}$

Now you can separate out the real and imaginary components using Euler's formula.
• October 27th 2008, 05:19 AM
philyc86
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• October 27th 2008, 05:39 AM
shawsend
Ok, sorry. I made a mistake. It's:

$-\frac{i}{1-i}\left(\frac{1+i}{1+i}\right)=-\frac{i(1+i)}{2}=\frac{1-i}{2}$

Also, Euler's Formula is $e^{a+ix}=e^a(\cos(x)+i\sin(x))$ and that's how you separate the real and imaginary components out if the number is in exponential form.