# Math Help - i

1. ## i

Let i be the complex number (0,1)

Show that i = (0,1) and (0, -1) are the only square roots of -1. Hint: Suppose that (x,y)(x,y) = (-1,0) and show that x = 0 and y = +-1. You can use the fact that, for real numbers, the only square roots of positive 1 are +-1. You also know that x^2 >= 0.

I have no idea what to do...Any advice?

2. Originally Posted by jzellt
Let i be the complex number (0,1)

Show that i = (0,1) and (0, -1) are the only square roots of -1. Hint: Suppose that (x,y)(x,y) = (-1,0) and show that x = 0 and y = +-1. You can use the fact that, for real numbers, the only square roots of positive 1 are +-1. You also know that x^2 >= 0.

I have no idea what to do...Any advice?
Hi

The rules of multiplication in $\mathbb{C}$ are
(x,y)(x',y') = (xx'-yy',xy'+x'y)

Therefore (x,y)(x,y) = (x²-y²,2xy)

Suppose that (x,y)(x,y) = (-1,0) then
x²-y² = -1
2xy = 0

I think you can finish now