# Math Help - Complex Numbers

1. ## Complex Numbers

Show that z = x + iy is pure imaginary if and only if $\overline z$ = -z

z = x +iy
- z = -x - iy

$\overline z$ = x - iy

x - iy = -x - iy
x = -x

Umm...yeah I don't know how this works. Can someone help?

2. Sorry my mistake before editing.

From where you left off...

2x = 0.

Therefore x = 0

So the value of x (the real part) is 0 for z. So z must be imaginary if -z = z's conjugate.