How do you evaluate # e^( ( 13 pi)/8 i) - e^( (7 pi)/3 i)# using trigonometric functions?

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Answer 1 · 2017-10-16T14:17:42

Use Euler's formula...

...which is:

#e^(itheta) = cos(theta) + isin(theta)#

...so you'd have:

#cos((13pi)/8) + isin((13pi)/8) - (cos((7pi)/3) + isin((7pi)/3))#

So, make sure your calculator is in "radians" mode instead of degrees. You get:

#0.383 -0.924i - 0.5 - 0.866i#

#= -0.117 - 0.058i#

GOOD LUCK