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Multiplication with Vectors

If ei θ=cosθ+...

Question

If $e^{i θ} = c o s θ + i s i n θ$ , then for the $△ A B C, e^{i A} . e^{i B} . e^{i C}$ is equal to

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
Hint: $a^{m} a^{n} = a^{m + n}$
$e^{i θ} = c o s θ + i s i n θ$
Solution: $e^{i A} e^{i B} e^{i C} = e^{i (A + B + C)} = e^{i n}$
$= c o s π + i s i n π$
$= - 1$

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