How can you use trigonometric functions to simplify $8 e^{\frac{π}{8} i}$ $8 e^( ( pi)/8 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify $8 e^{\frac{π}{8} i}$ $8 e^( ( pi)/8 i )$ into a non-exponential complex number?

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Answer 1 · 2016-04-16T08:57:30

$7.392 + 3.064 i$ $7.392 + 3.064i$

Explanation:

According to Euler's formula,

$e^{i x} = cos x + i sin x$ $e^(ix) = cosx + isinx$ .

Inserting the value $x = \frac{π}{8}$ $x = pi/8$ from the equation, then

$e^{\frac{π}{8} i} = cos (\frac{π}{8}) + i sin (\frac{π}{8})$ $e^(pi/8i) = cos(pi/8) + isin(pi/8)$
$= cos 22.5 + i sin 22.5$ $= cos22.5 + isin22.5$
$= 0.924 + 0.383 i$ $= 0.924 + 0.383i$ .

Multiplying all this by $8$ $8$ as in the question, and

$8 e^{\frac{π}{8} i} = 7.392 + 3.064 i$ $8e^(pi/8i) = 7.392 + 3.064i$

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How can you use trigonometric functions to simplify $8 e^{\frac{π}{8} i}$ $8 e^( ( pi)/8 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify $8 e^{\frac{π}{8} i}$ $8 e^( ( pi)/8 i )$ into a non-exponential complex number?