The complex number $q$ is given by $q=\frac{{{e}^{i\theta }}}{1-{{e}^{i\theta }}}$, where \

Question

The complex number $q$ is given by $q=\frac{{{e}^{i\theta }}}{1-{{e}^{i\theta }}}$, where $0 < \theta \le 2\pi $. find the real part of $q$, show that the imaginary part of $q$ is $\frac{1}{2}\cot \left( \frac{1}{2}\theta \right)$.

Accepted Answer

(i) Re(q) = −1/2; (ii) Im(q) = ½ cot(θ/2) (shown)

N1998 P2 Q12

N1998 P2 Q12

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