How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{19 π}{12} i}$ $e^( ( 7 pi)/4 i) - e^( ( 19 pi)/12 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{19 π}{12} i}$ $e^( ( 7 pi)/4 i) - e^( ( 19 pi)/12 i)$ using trigonometric functions?

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Answer 1 · 2016-11-27T08:09:29

In complex terms, $R (sin θ + i cos θ)$ $R ( sintheta + i costheta )$ = $R e^{i θ}$ $Re ^ (i theta)$
where $R$ $R$ is the modulus and $θ$ $theta$ is the argument.

So
$e^{\frac{7 π}{4} i} - e^{\frac{19 π}{12} i}$ $e^( ( 7 pi)/4 i) - e^( ( 19 pi)/12 i)$ = $1 (\frac{sin (7 π)}{4} + i \frac{cos (7 π)}{4})$ $1 ( sin ( 7pi)/4 + i cos ( 7pi)/4 )$
- $1 (\frac{sin (19 π)}{12} + i \frac{cos (19 π)}{12})$ $1 ( sin ( 19 pi)/12 + i cos ( 19 pi)/12 )$

= $\frac{sin (7 π)}{4} + i \frac{cos (7 π)}{4}$ $sin ( 7pi)/4 + i cos ( 7 pi)/4$
- $\frac{sin (19 π)}{12} + i \frac{cos (19 π)}{12}$ $sin ( 19 pi)/12 + i cos ( 19 pi)/12$

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How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{19 π}{12} i}$ $e^( ( 7 pi)/4 i) - e^( ( 19 pi)/12 i)$ using trigonometric functions?

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