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Question

Number of value of $z$ for which $sin z = 0$ is

0

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Infinite

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Solution

The correct option is D Infinite
$\frac{1}{2 i} (e^{i x} - e^{- i x})$
Multiplying and by i
$= \frac{i}{2} (e^{- i x} - e^{i x})$
$= 0$
$e^{- i x} - e^{i x} = 0$
$e^{i x} = e^{- i x}$
$e^{i 2 x} = e^{i 2 k π}$
Hence
$x = k π$ ...( $k ϵ N$ )
Hence infinite values.

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