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How can you use trigonometric functions to simplify # 13 e^( ( pi)/8 i ) # into a non-exponential complex number?

Answer 1

Asher Friedman

#13 [ cos(pi/8) + isin(pi/8) ]#

Using #color(blue)" Euler's relation"#

which states #re^(theta i) = r(costheta + isintheta )#

here r = 13 and #theta = pi/8 #

#rArr 13e^(pi/8 i) = 13 [ cos(pi/8) + isin(pi/8) ] #

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Answer 2

Zoe Austin

You can use Euler's formula, ( e^{ix} = \cos(x) + i \sin(x) ), to rewrite ( e^{\frac{\pi}{8}i} ) in terms of trigonometric functions. Then, you can simplify the expression accordingly.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.