How do you evaluate $e^( ( 3 pi)/8 i) - e^( ( 7 pi)/4 i)$ using trigonometric functions?

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Answer 1 · 2018-05-30T10:40:26

$e^((3 pi)/8 i)-e^((7 pi)/4 i) ~~ -0.324 + 0.217 i$

$e^((3 pi)/8 i) - e^((7 pi)/4 i) = ?$

We know $e^(itheta) = cos theta +i sin theta$

$(3 pi)/8 =(3*180)/8= 67.5^0 , (7 pi)/4= (7*180)/4 = 315.0^0$

$cos 67.5 ~~0.383 ; sin 67.5 = 0.924 ; cos 315 ~~ 0.707 ;$

$sin 315.0 ~~ -0.707$

$e^((3 pi)/8 i)= cos 67.5 + sin 67.5*i=0.383 + 0.924 i$

$e^((7 pi)/4 i) = cos 315 + sin 315*i=0.707 - 0.707 i$

$e^((3 pi)/8 i)-e^((7 pi)/4 i)~~(0.383 + 0.924 i)-(0.707 - 0.707 i)$

or $e^((3 pi)/8 i)-e^((7 pi)/4 i) ~~ -0.324 + 0.217 i$ [Ans[

How do you evaluate e^( ( 3 pi)/8 i) - e^( ( 7 pi)/4 i)e^( ( 3 pi)/8 i) - e^( ( 7 pi)/4 i) using trigonometric functions?