Question

Calculate the square roots of the complex number 5 - 12i. ps.:the result is 3 - 2i; -3 + 2i but how can I do it?

Answer 1

\[(a+bi)^2=5-12i\]

\[a^2-b^2+2abi=5-12i\]

solve

\[a^2-b^2=5\] and \[2ab=12\]

for a,b

Answer 2

2ab=-12