Vaibhav P.

asked • 05/14/16

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
 
Report

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
 
 
Report

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
Report

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
 
Report

05/14/16

1 Expert Answer

By:

Hassan H. answered • 05/16/16

Tutor
5.0 (176)

Math Tutor (All Levels)

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.
Report

05/19/16

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.