z^4=-32/(1+isqr3)

To find the 4 roots of a complex number, the first step is to find the polar form as

z=r(cos x +i sin x) where “x” is the angle in degrees or radians.

Let us try to represent the -32/(1+isqr3) in the polar form. Let us rationalize the denominator (1+isqr3)

z^4=-32/(1+isqr3)

=>

Multiplying and dividing the side side of “=” by 2 we get

=>

=>

=>Taking 4th power both sides.

=>

=>

Now we plug n=0,1,2,3 to get 4 roots.

When n=0

when n=1

When n=2

when n=3

Therefore the four roots of

are

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