# Math Help - finding z1 , z2 of complex numer

1. ## finding z1 , z2 of complex numer

in order to get z1 and z2 , i tried to express z^2 into polar form, but z is to the power of 2, i'm not sure whether it can be epressed in polar form of not. by the way , here's my working. how should i proceed? i dont think my ans is correct.

2. ## Re: finding z1 , z2 of complex numer

Originally Posted by delso
in order to get z1 and z2 , i tried to express z^2 into polar form, but z is to the power of 2, i'm not sure whether it can be epressed in polar form of not. by the way , here's my working. how should i proceed? i dont think my ans is correct.
Please learn some basic LaTeX. It is hard enough to read from an image,

3. ## Re: finding z1 , z2 of complex numer

$\text{Arg}(1-2\sqrt 2 i)=\arctan(-2 \sqrt 2)=\theta$

${z_1} = \sqrt 3 \exp \left( {\frac{\theta }{2} } \right)\;\& \;{z_2} = \sqrt 3 \exp \left( {\frac{\theta+\pi }{2 }} \right)$

4. ## Re: finding z1 , z2 of complex numer

Originally Posted by Plato
$\text{Arg}(1-2\sqrt 2 i)=\arctan(-2 \sqrt 2)=\theta$

${z_1} = \sqrt 3 \exp \left( {\frac{\theta }{2} } \right)\;\& \;{z_2} = \sqrt 3 \exp \left( {\frac{\theta+\pi }{2 }} \right)$
can you please show me how do u express z^2 in polar form step by step, i have done it in the very first post, but i dont think it's correct. my ans is weird. i cant understand your working in post 3