Question

find a square root of -7-24i

Answer 1

referring to a standard 7-24-25 right triangle,

(x,y) = (-7,-24)
(r,θ) = (25,π+arctan(24/7)) = (25,4.4286)
square root:
(r,θ) = (5,2.2143)
(x,y) = (-3,4)
= -3 + 4i