# Math Help - Finding roots of complex numbers

1. ## Finding roots of complex numbers

The question:

i) Find the complex square roots of -24-10i by solving $(x+iy)^2 = -24-10i$ for x, y real.

ii) Hence, find the roots of the quadratic $z^2-(1+i)z + (6+3i)$ in "a+ib" form where a, b are real numbers.

My attempt:
i) I got the answer $\pm(1-5i)$
ii) This is where I have trouble. The question appears to suggest that I use the result of part i) to solve part ii). I'm not sure how they relate. I was thinking of using the quadratic formula, but perhaps there's a quicker way?

Any assistance would be greatly appreciated!

2. I think, unless you can factor the quadratic by heart, the quadratic formula is the best way to go.
This relates to i) as follows: In the quadratic formula, you will need to calculate the roots of the discriminant. You learned this in i)

3. Ahh, I see. Thank you!