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# Express [(z/w*)^6]-[(z*/w)^6] in a+bi ?

Express [(z/w*)^6]-[(z*/w)^6] in a+bi , where a, b are real numbers and

z= -1+ i,

w= -√3 + i

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- mathematicianLv 71 decade agoFavorite Answer
Write z and w* in polar form:

z=sqrt(2)exp(i*3pi/4)

w*=2exp(i*7pi/6).

Then z/w* is easily obtained in polar form. Raise it to the 6th power

to find

(z/w*)^6=-(1/8)i.

But (z*/w) is the complex conjugate of z/w*, so the final answer will be twice the imaginary part of this result: -(1/4)i.

- Anonymous1 decade ago
I wish! I failed math twice in high school. All the best with your puzzle.

- Anonymous1 decade ago
Can we have pancakes now...

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