How can you use trigonometric functions to simplify $3 e^{\frac{3 π}{2} i}$ $3 e^( ( 3 pi)/2 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify $3 e^{\frac{3 π}{2} i}$ $3 e^( ( 3 pi)/2 i )$ into a non-exponential complex number?

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Answer 1 · 2015-12-29T21:23:03

Use the Moivre formula.

Explanation:

The Moivre formula tells us that $e^{i \cdot n x} = cos (n x) + i sin (n x)$ $e^(i*nx) = cos(nx) + isin(nx)$ . You apply it to the exponential part of this complex number.

$3 e^{i \frac{3 π}{2}} = 3 (cos (\frac{3 π}{2}) + i sin (\frac{3 π}{2})) = 3 (0 - i) = - 3 i$ $3e^(i(3pi)/2) = 3(cos((3pi)/2) + isin((3pi)/2)) = 3(0 - i) = -3i$ .

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How can you use trigonometric functions to simplify $3 e^{\frac{3 π}{2} i}$ $3 e^( ( 3 pi)/2 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify $3 e^{\frac{3 π}{2} i}$ $3 e^( ( 3 pi)/2 i )$ into a non-exponential complex number?