Question

Find the root square root of -15 - 18i

Answer 1

let x+iy be square root of-15 - 18i
then (x+iy)^2=-15 - 18i
⇒x^2-y^2=-15
2xy=-18 0r xy=-9

solving these equation for x and y we get
x=   -2.053137724036062 or    2.053137724036062
and y=4.383534477320782 or -4.383534477320782
hence roots are
 -2.053137724036062   +  i* 4.383534477320782
and 2.053137724036062   +  i* -4.383534477320782