Hi MHF

I'm writing my AdMath exam in a few days, so I went through previous years' tests and found a problem that I just can't solve!

It goes like this:

The sum of two complex numbers is 0. The product of these two numbers is 4. What are the two numbers?

At first I thought of doing a simultaneous equation , then I tried using conjugates ... nothing works.

I spent a few hours trying to solve it, using every method I could. Is this a trick question or am I just missing something simple?

Please help!