How can you use trigonometric functions to simplify $28 e^{\frac{3 π}{2} i}$ $28 e^( ( 3 pi)/2 i )$ into a non-exponential complex number?

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Answer 1 · 2016-03-02T11:38:37

$- 28 i$ $-28i$

One can use here $e^{i x} = cos x + i sin x$ $e^(ix)=cosx+isinx$

Hence $28 e^{\frac{3 π}{2} i} = 28 (cos (\frac{3 π}{2}) + i sin (\frac{3 π}{2}))$ $28e^((3pi)/2i)=28(cos((3pi)/2)+isin((3pi)/2))$

or $28 (0 + i (- 1))$ $28(0+i(-1))$ or $- 28 i$ $-28i$

How can you use trigonometric functions to simplify 28e3π2i 28 e^( ( 3 pi)/2 i ) into a non-exponential complex number?