How can you use trigonometric functions to simplify $23 e^( ( pi)/8 i )$ into a non-exponential complex number?

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Answer 1 · 2016-04-08T15:11:50

$23e^(pi/8i) = - 20.08 - 11.2i$

According to Euler's formula,

$e^(ix) = cosx + isinx$ .

When $pi/8$ is substituted as $x$ , then

$e^(pi/8i) = cos(pi/8) + isin(pi/8)$
$= cos(22.5^o) + isin(22.5^o)$
$= -0.873 -0.487i$ ,

which is the value of $e^(pi/8i)$ .

Multiply the whole thing by $23$ to find the entire thing:

$23(- 0.873 - 0.487i) = - 20.08 - 11.2i$

How can you use trigonometric functions to simplify 23 e^( ( pi)/8 i ) 23 e^( ( pi)/8 i ) into a non-exponential complex number?