Question

(x+iy)^2=8i

Answer 1

There are a couple of ways to skin this cat. Here's one.

Note first that:

(x+iy)^2 = (x^2 - y^2) + 2xyi

So if that is equal to 8i then, settling real and imaginary parts equal,

x^2 - y^2 = 0
2xy = 8

The first of these equations means that x = +y or -y.

Now I'll let you take it from here. Remember that x and y have to be real numbers themselves.