- #1

renvox

- 10

- 0

## Homework Statement

Hi,

I have to solve this exercise:

"Given that (a+bi)^2 = 3+4i obrain a pair of simultaneous equations involving a and b. Hende find the two square roots of 3+4i. Hence find the two suqre roots of 3+4i."

I don't really know to do do it.

**2. The attempt at a solution**

Well, that's what I thought:

(a+bi)^2 = 3+4

we expand:

a^2+2abi-b^2=3+4i

we group them:

2abi-4i=-a^2+b^2+3

common factor:

2i(ab-2)=-ab^2+b^2+3

2i=(-a^2+b^2+3)/(ab-2)

And now I don't even know if what I've done is good, and if it's good what should be the next step?