SOLUTION: find the three cube roots of 6-2i and express the roots in polar form.

Question 1170262: find the three cube roots of 6-2i and express the roots in polar form.
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
find the three cube roots of 6-2i and express the roots in polar form.
First we plot the point 6-2i which is the point (6,-2), x=6, y=-2
We draw a vector from(0,0) to (6,-2).

The hypotenuse is , but we'll leave it for now.
Calculate θ by , so

So 6-2i in polar form is

We can add any integer times 360° to the angle without changing the value:

We raise both side to the 1/3 power, the same as taking cube root, and write
as the 1/2 power of 40

Next we use DeMoivre's theorem, which is to raise the modulus to the 1/3
power and multiply the argument by 1/3:

where n=0,1,2
[Write all three values out].
Or if you want it in radians, substitute for 120°
Edwin

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