Question

z is a complex number , then if |z| is given then doing |z|^2 = z (this is a real number only) can l substitute this real number value for z in z^2 where z looks like x+yi .

Basically is x^2+y^2 = (x+yi)^2 ??

Answer 1

let z= x+iy
z^2 = (x+iy)^2 = x^2 + 2.x.iy + (iy)^2
=x^2 + i^2 .y^2 +i . 2xy
=x^2-y^2 + i .2xy

|z|^2 = |x+iy|^2 = x^2 +y^2

i think you got the idea . this s the corect one.

Like if satisifed