If z = 1 –StartRoot 3 EndRoot i, what is z^3? please help im stressed a) -8

b) 8

c) -8i

d) 8i

Correct a) -8

Step-by-step explanation:

Complex Numbers

A complex number z in polar form is expressed as

The nth power of a complex number in polar form is:

If the complex number is given in rectangular form

then the values of r and θ are given by:

The given complex number is:

The value of r is:

r=2

Calculating the angle:

Since the number is in the quadrant IV, the angle is:

Thus, z is expressed in polar form as:

Calculating:

Given cos 180°=-1 and sin(-180°)=0

Correct a) -8