How do you evaluate $2 e^{\frac{3 π}{8} i} - 3 e^{\frac{7 π}{8} i}$ $2 e^( ( 3 pi)/8 i) - 3e^( ( 7 pi)/8 i)$ using trigonometric functions?

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Answer 1 · 2018-06-07T11:59:10

$: 2 e^{\frac{3 π}{8} i} - 3 e^{\frac{7 π}{8} i} \approx (3.54 + 0.70 i)$ $:2 e^((3 pi)/8 i)- 3 e^((7 pi)/8 i)~~( 3.54+0.70 i)$

$2 e^{\frac{3 π}{8} i} - 3 e^{\frac{7 π}{8} i}$ $2 e^((3 pi)/8 i)- 3 e^((7 pi)/8 i)$

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

$\frac{3 π}{8} \approx 1.178097, \frac{7 π}{8} \approx 2.748893$ $(3 pi)/8 ~~ 1.178097 , (7 pi)/8 ~~ 2.748893$

$:. 2 e^((3 pi)/8i) = 2(cos ((3 pi)/8)+ i sin ((7 pi)/8))$

$=0.765367+ 1.847759 i$

$:. 3 e^((7 pi)/8 i) = 3(cos ((7 pi)/8)+ i sin ((7 pi)/8))$

$~~ -2.77164 + 1.14805 i$

$:.2 e^((3 pi)/8 i)- 3 e^((7 pi)/8 i)$

$~~(0.765367+ 1.847759 i)- ( -2.77164 + 1.14805 i)$

$~~( 3.54+0.70 i) (2 dp)$ [Ans]

How do you evaluate 2 e^( ( 3 pi)/8 i) - 3e^( ( 7 pi)/8 i)2e3π8i−3e7π8i 2 e^( ( 3 pi)/8 i) - 3e^( ( 7 pi)/8 i) using trigonometric functions?