Question

Find the square root of the complex number

(a)5+12i

Please help

Answer 1

We want to find two real numbers p and q such that (p+qi)(p+qi)=(5+12i). Collect the real and the imaginary terms together into two separate equations:

Real terms: p²-q²=5
Imaginary terms: 2pq=12, i.e. pq=6

You could solve the above as a pair of simultaneous equations, but trial and error is probably faster: what you should find is that p=3 and q=2, which gives you the answer you're looking for.