Hello everyone,

Let w be one of the three complex numbers having the property that

w^3 = -4 + 4*sqrt(3)i.

What is the |w|?

Also if a = 2Re(w) how can one show that a is a root of the polynomial:

p(z) = z^3 - 12z + 8.

Thanks for your time.

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- Sep 17th 2010, 12:12 PMJoAdams5000Complex Numbers and Cubic Polynomial Roots
Hello everyone,

Let w be one of the three complex numbers having the property that

w^3 = -4 + 4*sqrt(3)i.

What is the |w|?

Also if a = 2Re(w) how can one show that a is a root of the polynomial:

p(z) = z^3 - 12z + 8.

Thanks for your time.

- Sep 17th 2010, 01:15 PMPlato
First note that $\displaystyle \left| {z^3 } \right| = \sqrt {16 + 48} = 8$. So $\displaystyle |z|=?$

I do not follow the second part of the question.

Is it related to first part? - Sep 17th 2010, 01:45 PMArchie Meade
- Sep 17th 2010, 02:07 PMJoAdams5000
Thanks!

Part b is related to the first part, so

**a**= 2*Re(w) where w is the be one of the three complex numbers having the property that w^3 = -4 + 4*sqrt(3)i.

Then I must show that**a**is a root of the polynomial z^3 - 12*z + 8.

And the polynomial is p(z) = z^3 - 12z + 8

Thanks in advance. - Sep 17th 2010, 02:21 PMmr fantastic