complex number equation

[cursive vapor]

z ^ 2 = |z|, with z being a complex number. How can i solve this? i have no idea.

[river ivy]

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[twilit basalt]

well you see

z = x + iy for reals x, y

the rest follows naturally

[cursive vapor]

yes i know, i tried it, but you kinda get (x + iy) ^ 2 = sqrt(x ^ 2 + y ^ 2)

so like (x + iy) ^ 4 = x ^ 2 + y ^ 2

[icy whale]

First of all, |z| is a non-negative real number

Which restricts z

(z^2 is non-negative real if z is ...)

[cursive vapor]

ok i got it

finally solved it

thx

+close