If $\left| {z - i} \right| = 1$ and $\arg \left( z \right) = {\rm{\theta }},$ where $0 < {\rm{\theta }} < \frac{\pi }{2}$, then $\cot {\rm{\theta }} - \frac{2}{z}$ equals

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

\left| {z - i} \right| = 1

and

\arg \left( z \right) = \mathrm{\theta },

where

0 < \mathrm{\theta } < \frac{\pi }{2}

, then

\cot \mathrm{\theta } - \frac{2}{z}

equals

View answer and explanation

Correct option: C

i

Option C (

i

) is correct because after substituting

z = r(\cos \theta + i\sin \theta )

and simplifying using the given condition

|z - i| = 1

, the expression

\cot \mathrm{\theta } - \frac{2}{z}

simplifies to

i

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