Question

Find the square root of ($-15-8i$).

Answer 1

We need to find the square root of $-15-8i$

$-15-8i=(-16)-8i+1=(4i{)}^2-(2\cdot 4i\cdot 1)+(1{)}^2=(4i-1{)}^2$

$\therefore -15-8i=(4i-1{)}^2$

Hence square root of $-15-8i$ is $\pm (4i-1)$