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Euler's Representation

If eiθ = cos ...

Question

If $e^{i θ} = c o s θ + i s i n θ,$ then in $△ A B C$ value of $e^{i A} . e^{i B} . e^{i C}$

A

-i

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B

1

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C

-1

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D

None of these

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Solution

The correct option is C -1
$e^{i A} . e^{i B} . e^{i C} = e^{i A + i B + i C} = e^{i (A + B + C)} = e^{i π}$
$[∴ A + B + C = π]$
$= c o s π + i s i n π = (- 1) + i (0) = - 1.$

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