How can you use trigonometric functions to simplify $21 e^{\frac{π}{2} i}$ $21 e^( ( pi)/2 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify $21 e^{\frac{π}{2} i}$ $21 e^( ( pi)/2 i )$ into a non-exponential complex number?

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Answer 1 · 2016-03-03T02:19:59

$21 e^{i (\frac{π}{2})} = 21 i$ $21 e^{i (pi/2)} = 21 i$

Explanation:

There is this identity which is very useful.

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

In this case,

$r = 21$ $r = 21$

$θ = \frac{π}{2}$ $theta = pi/2$

So plugging the values in

$21 e^{i \frac{π}{2}} = 21 (cos (\frac{π}{2}) + i sin (\frac{π}{2}))$ $21 e^{i pi/2} = 21 (cos (pi/2) + i sin (pi/2))$

$= 21 ((0) + i (1))$ $= 21 ((0) + i (1))$

$= 21 i$ $= 21 i$

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How can you use trigonometric functions to simplify $21 e^{\frac{π}{2} i}$ $21 e^( ( pi)/2 i )$ into a non-exponential complex number?

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Explanation:

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How can you use trigonometric functions to simplify 21eπ2i 21 e^( ( pi)/2 i ) into a non-exponential complex number?

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How can you use trigonometric functions to simplify $21 e^{\frac{π}{2} i}$ $21 e^( ( pi)/2 i )$ into a non-exponential complex number?