Complex Roots

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greatwhiteshark

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May 8, 2005
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I practiced the even number questions in my textbook. The book does not list the answers for even numbers in the back. Only odd number answers are given. I am only going to give you my answers for 2 questions. Can you please check to see if I correct?

1) Find the complex cube roots of -8 - 8i.

My Answers: d = degrees

First root = 16^1/6 (cos 75d + i sin 75d)

Second root = 16^1/6 (cos 195d + i sin 195d)

Third root = 16^1/6 (cos 315d + i sin 315d)

2) Find the complex cube roots of -8.

First root = 2(cos0d + i sin0d)

Second root = 2(cos 120d + i sin 120d)

Third root = 2(cos 240d + i sin 240d)

Am I right? If not, can you help me by providing the steps that will guide me through?
 
cpxroots0vf.gif
 
pka

You did not explain question 2. So, I assume that I got it right.
Tell me, do you have a special keyboard? How do you come up with special math notations?
 
tkhunny

I did not select -135 degrees as the initial degree. Tutor pka solved the question. Are you saying the the correct degree amount should 225?
How? Why?
 
“Why did you pick -135º instead of +225º.”
Just out of habit!

When I teach Complex Variables, I insist that all answers be written with the argument be between –pi and pi (by the way, NOT in degrees).
 
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