Number of value of $z$ for which $e^{z} = 0$ is

0

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1

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Infinite

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Solution

The correct option is A $0$
Let $e^{z} = 0$
Then $e^{x} (cos y + i sin y) = 0$
$e^{x} \neq 0$ for any $x \in R$
So $cos y + i sin y$ has to be zero.
For this both $cos y$ and $sin y$ has to be zero. This is not possible.
Hence number of value of $z$ for which $e^{z} = 0$ is zero.

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