We have, e^iθ= cosθ+isinθ ⇒ e^2+i=e^2· e^i =e^2(cos 1 + i sin 1) ...

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Standard XII

Mathematics

Euler's Representation

The value of ...

Question

The value of $e^{2 + i}$ is

Name: JEE- Grade 11- Mathematics- Complex Numbers- Session 04- D01
Uploaded: 2022-07-04T10:36:42+05:30
Description: We have, e^iθ= cosθ+isinθ ⇒ e^2+i=e^2· e^i =e^2(cos 1 + i sin 1) ...

e [cos 1 + i sin 1]

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e^{2} [cos 1 + i sin 1]

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cos 1 + i sin 1

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e^{- 2} [cos 1 + i sin 1]

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Solution

The correct option is B $e^{2} [cos 1 + i sin 1]$
We have, $e^{i θ} = cos θ + i sin θ$
$\Rightarrow e^{2 + i} = e^{2} \cdot e^{i} = e^{2} (cos 1 + i sin 1)$

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Euler's Representation

Standard XII Mathematics

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The value of e2+i is

The correct option is B e2[cos1+isin1]We have, eiθ=cosθ+isinθ ⇒e2+i=e2⋅ei=e2(cos1+isin1)

The value of $e^{2 + i}$ is

The correct option is B $e^{2} [cos 1 + i sin 1]$
We have, $e^{i θ} = cos θ + i sin θ$
$\Rightarrow e^{2 + i} = e^{2} \cdot e^{i} = e^{2} (cos 1 + i sin 1)$