Friday, 11 October 2013

complex number

Let z be a complex number such that z & (z + 1) have modulus 1. If for a positive integer n, (z + 1) be an nth. root of unity, then show that z is an nth. root of unity and n is a multiple of 6.
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Define f:R→R by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \ 0, ...