How do you evaluate $2 e^( ( 3 pi)/8 i) - 5 e^( ( 19 pi)/8 i)$ using trigonometric functions?

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Answer 1 · 2018-04-26T11:59:33

$:. 2 e^((3 pi)/8 i)- 5 e^((19 pi)/8 i) ~~-1.15 -2.77 i$

$2 e^((3 pi)/8 i)- 5 e^((19 pi)/8 i)$

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

$(3 pi)/8 ~~ 1.178097 , (19 pi)/8 ~~ 7.461823$

$:. 2 e^((3 pi)/8i) = 2(cos ((3 pi)/8)+ i sin ((3 pi)/8))$

$=0.765367+ 1.847759 i$

$:. 5 e^((19 pi)/8 i) = 5(cos ((19 pi)/8)+ i sin ((19 pi)/8))$

$~~ 1.913417 + 4.619397 i$

$:. 2 e^((3 pi)/8 i)- 5 e^((19 pi)/8 i)$

$=(0.765367+ 1.847759 i)- (1.913417 + 4.619397 i)$

$=( -1.148050- 2.771638 i)$

$:. 2 e^((3 pi)/8 i)- 5 e^((19 pi)/8 i) ~~-1.15 -2.77 i (2 dp)$ [Ans]

How do you evaluate 2 e^( ( 3 pi)/8 i) - 5 e^( ( 19 pi)/8 i) 2 e^( ( 3 pi)/8 i) - 5 e^( ( 19 pi)/8 i) using trigonometric functions?