Vaibhav P.

# This is a question from complex numbers.

If 1,w and w2 are the three cube roots of unity and a,b and c are the cube roots of p,q (<0),then for any x,y and z,the expression {(xa + yb + zc)÷(xb + yc + za)} is equal to ?

Hassan H.

Vaibhav,

What do you mean by the part "...and a, b and c are the cube roots of p,q (<0)?  Specifically, what does p,q (<0) mean in context?

-Hassan

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05/14/16

Vaibhav P.

Hassan,

I don't know.That's what the question written in my textbook.I'm just stuck at it.

-Vaibhav

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05/14/16

Hassan H.

Vaibhav,

The reason I ask is because I don't know if p and q are supposed to be complex, or simply real, or are they the real and imaginary parts of a complex number, or what?  And since every complex number has, as you know, three cube roots, I don't see how I am supposed to relate three numbers a, b, and c, to the cube roots of two numbers p and q, and also, to what the condition (<0) applies.

Does your book perhaps refer to p and q in a previous problem, or in the body of the text in some specific way?

-Hassan
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05/14/16

Vaibhav P.

Hassan,

The solution in the book :-

Because, p<0 ,take p=-q3(q>0)
Therefore, p1/3=q(-1)1/3=-q,-qw,-qw2
Thus,      a=-q,b=-qw,c=-qw2
Therefore, given expression = w2

But I can't understand what's going on in the solution.
Can you help me?

-vaibhav

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05/14/16

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Vaibhav P.

Hassan,
Thanks,actually I also forgot about the question but now I definitly got what's going on in this question.
Thanks again.
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05/19/16

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