How do you evaluate # e^( ( 19 pi)/12 i) - e^( (3 pi)/4 i)# using trigonometric functions?

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Answer 1 · 2016-04-09T13:20:58

#0.363 + 0.686i#

According to Euler's formula,

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

Substituting the different values for #x# in the question,

#e^((19pi)/12i) = cos((19pi)/12) + isin((19pi)/12)#
# = cos285 + isin285#
# = - 0.633 + 0.774i#

#e^((3pi)/4i) = cos((3pi)/4) + isin((3pi)/4)#
# = cos135 + isin135#
# = - 0.996 + 0.088i#

Using these values, the final answer is

#e^((19pi)/12i) - e^((3pi)/4i) `= - 0.633 + 0.774i + 0.996 - 0.088i#
# = 0.363 + 0.686i#