Question

If w is complex cube root of the unity then find the value of 1/w+1/w^2

Answer 1

If w is one of the complex cube roots of unity, how can we show that 1+w equals 1?

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3 ANSWERS



Shivam Gupta, I am better with the old integers.

Answered Jan 25 2015

You mean to say: 1 + w + w^2 =0

Since ,w is cube root of unity, hence by definition.

w^3 = 1
w^3 = 1^3

w^3 - 1^3 = 0
By identity relations in algebra.

(w -1)(1 + w + w^2) = 0

Since, w is not equal to 1, hence what you asked for is proved.