Find the two square roots of −4i

Question

Find the two square roots of −4i .(Give your answers in the form a + bi, where a and b are real numbers. Enter your answers as a comma-separated list.)

Answer 1

Hailey, I am available for tutoring and I am smart in complex domains and functions.

make(-4*i)^(1/2) into (4*(cos(-π/2+2πk)+i*sin(-π/2+2πk))^(1/2)=z₁ and z₂ , k=0,1

using DM theorem, z= +/-2*(cos (-π/4+πk)+i*sin(-π/4+πk) k=0,1

z₁= √2-i*√2

z₂= -√2+i*√2

since z₁= -z₂, the+/- piece in front of 2 from the square root of 4 becomes moot

you can check, z₁² and z₂² both =- -4*i

Answer 2

±sqrt(2)(-1+i)/2 are the 2 square roots