If $z = r\;{e^{i\;{\rm{\theta }}}},$ $\left| {{e^{i\;z}}} \right|$ is equal to

${e^{ - r\sin {\rm{\theta }}}}$

$r\;{e^{ - r\sin {\rm{\theta }}}}$

${e^{ - r\cos {\rm{\theta }}}}$

$r\;{e^{ - r\cos {\rm{\theta }}}}$

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

z = r\;{e^{i\;\mathrm{\theta }}},

\left| {{e^{i\;z}}} \right|

is equal to

View answer and explanation

Correct option: A

{e^{ - r\sin \mathrm{\theta }}}

Option A (

{e^{ - r\sin \mathrm{\theta }}}

) is correct because it is derived from Euler's formula and properties of complex exponentials.

Practice All Chapter MCQs →

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