Find the value of $z \in\mathbb C$ such that $|z| - z = 5+9i$ express answer in exact form.

Question

Find the value of $z \in\mathbb C$ such that $|z| - z = 5+9i$ express answer in exact form.

Answer 1

Let $$z=x+iy$$ then your equation is equal to $$\sqrt{x^2+y^2}-x-iy=5+9i$$ You will get $$\sqrt{x^2+y^2}-5-x-i(9+y)=0$$