find all z values

metlx · #1 $Old$ November 1st, 2009, 11:47 AM

find all values for z for the following equation:

$z^2 + 2iRe(z) = |z|$

I tried
$|z|^2 \cdot (cos 2\phi + i \cdot sin 2\phi) + 2i \cdot a = |z|$

$|z| \cdot (cos 2\phi + i \cdot sin 2\phi) + \frac{2i \cdot a}{|z|} = 1$

what do i do now? can someone show me how to continue (or solve it if possible)?

tonio · #2 $Old$ November 1st, 2009, 08:33 PM

Quote:

Originally Posted by metlx $View Post$

find all values for z for the following equation:

$z^2 + 2iRe(z) = |z|$

I tried
$|z|^2 \cdot (cos 2\phi + i \cdot sin 2\phi) + 2i \cdot a = |z|$

$|z| \cdot (cos 2\phi + i \cdot sin 2\phi) + \frac{2i \cdot a}{|z|} = 1$

what do i do now? can someone show me how to continue (or solve it if possible)?

Put z = x + yi, so your equation is:

$x^2-y^2+2x(y+1)i =\sqrt{x^2+y^2}$ , and compare real and imaginary parts:

$==\,\,x^2-y^2=\sqrt{x^2+y^2}$
$==\,\,2x(y+1)=0\Longrightarrow x=0\,\,or\,\,y=-1$ and etc.

Tonio