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Logarithm of a Complex Number

What is the v...

Question

What is the value of sin( ${l o g}_{e} i^{i})$ ?

A

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B

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C

-1

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D

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Solution

The correct option is C
-1

sin( ${l o g}_{e} i^{i})$

= sin( $i {l o g}_{e} i)$

Express complex number in Euler's form

= sin $[i {l o g}_{e} e^{i \frac{π}{2}}]$

= sin $(i . \frac{i π}{2})$

= sin $(- \frac{π}{2})$

=-1

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