Question

find all complex numbers z satisfying z=z^2​

Answer 1

Answer:

When z∈C:

|z+2i|=|(ℜ[z]+ℑ[z]i)+2i|=|ℜ[z]+(2+ℑ[z])i|=√ℜ2[z]+(2+ℑ[z])2

|z−2|=|(ℜ[z]+ℑ[z]i)−2|=|(ℜ[z]−2)+ℑ[z]i|=√(ℜ[z]−2)2+ℑ2[z]

So:

|z+2i|=|z−2| ⟺ √ℜ2[z]+(2+ℑ[z])2=√(ℜ[z]−2)2+ℑ2[z]