How do you evaluate $e^( ( 23 pi)/8 i) - e^( ( 19 pi)/6 i)$ using trigonometric functions?

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Answer 1 · 2018-08-05T11:10:52

$color(green)(e^((23pi)/8i) - e^((19pi)/6i) = -0.0579 + 0.8827 i, " IIQuadrant"$

Trigonometric form of $e^ (ix)$ , using Euler's Equation, is given by

$e^ (ix) = cos x + i sin x$

$e^((23pi)/8i) = ( cos((23pi)/8) + i sin((23pi)/8))$

$=> -0.9239 + i 0.3827, " II Quadrant"$

$e^((19pi)/6i) = cos((19pi)/6) + i sin((19pi)/6))$

$=> -0.866 - i 0.5, " III Quadrant"$

$e^((23pi)/8i) - e^((19pi)/6i) = -0.9239 + i 0.3827 + 0.866 + i 0.5$

$color(green)(e^((23pi)/8i) - e^((19pi)/6i) = -0.0579 + 0.8827 i, " IIQuadrant"$

How do you evaluate e^( ( 23 pi)/8 i) - e^( ( 19 pi)/6 i) e^( ( 23 pi)/8 i) - e^( ( 19 pi)/6 i) using trigonometric functions?