# Finding roots of complex numbers

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• Aug 25th 2010, 02:26 AM
Glitch
Finding roots of complex numbers
The question:

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

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

My attempt:
i) I got the answer $\displaystyle \pm(1-5i)$
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!
• Aug 25th 2010, 04:47 AM
Pim
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)
• Aug 25th 2010, 04:57 AM
Glitch
Ahh, I see. Thank you!