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Expert: Jack Cheng - 11/20/2006


Question
Hello. I have a guestion. Maybe you could help me? I will appreciate.Thank You


1) Find the principal root (-64)^1/6 . Express the result in the form a+bi

Thank You


Answer
Hi Piotr,

Well, to do this, you first have to separate it into:
(-1)^(1/6) * (64)^(1/6) = 2*(-1)^(1/6).

Now, I might be very wrong on this, but it seem right that:
(-1)^(1/6) = (-1)^(1/3)(1/2) = ((-1)^(1/3))^(1/2) = (-1)^(1/2) = i

So the answer is 2i.

Again, I am not sure about the last part. The math seems right, and 2i^6 is equaled to -64. However, my calculator somehow got 0.866+0.5i for (-1)^(1/6) (I did the ^(1/2) first and got i, then the cube root of it). It could be that there are two solutions, but I am not very sure. You should ask your teacher for more advice.

~ Jack

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Jack Cheng

Expertise

I can answer most questions in Math up to single-variable Calculus, including infinite series. I like to think very much, so questions with a lot of twists and turns are highly welcomed! Mathematical questions related to computer science are also highly welcomed! I can also answer some basic questions in discrete mathematics (logics, sets, some algorithms, basic number theory). I am also studying physics (mechanics in particluar), so I am willing to answer some questions relating to it.

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Majoring in Mathematics.

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I am sophomore/junior status in college working towards bachelor's degrees in Computer Science and Mathematics.

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