Math Analysis?

Question

Calculate ( 1 + i ) ^ 2. Use your result to find two square roots of "i"

Answer 1

(1 + i)^2 = 1^2 + 2i + i^2 = 1 + 2i + (-1) = 2i

From this, I guess it follows that i = ((1 + i)^2) / 2, and sqrt(i) = +/- (1 + i) / sqrt(2)

Answer 2

Multiplying it out, we get 1 + 2i + i*2, but the latter term is by definition -1. So the final result is 2i. From this, the square roots of i should be obvious.

Answer 3

Just multiply out (1+i)*(1+i) and see what happens.

Actually, you'll get a multiple of i.

So (1+i) must be a multiple of a square root of i.

Answer 4

( 1 + i ) ^ 2
(1+i)(1+i)
1+i+i+i^2
1+2i+i^2

i^2= -1

1+2i-1
=2i