What is the trigonometric form of $12 e^{\frac{π}{2} i}$ $12 e^( ( pi)/2 i )$ ?

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What is the trigonometric form of $12 e^{\frac{π}{2} i}$ $12 e^( ( pi)/2 i )$ ?

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Answer 1 · 2015-12-23T21:21:48

$12 i sin (\frac{π}{2})$ $12isin(pi/2)$

Explanation:

$12 e^{\frac{π}{2} i}$ $12e^(pi/2i)$ is an imaginary number only you see this because $A r g (z) = \frac{π}{2}$ $Arg(z) = pi/2$ which is on imaginary line only

So $12 e^{\frac{π}{2} i} = 12 (cos (\frac{π}{2}) + i sin (\frac{π}{2})) = 12 i sin (\frac{π}{2}) = 12 i$ $12e^(pi/2i) =12(cos(pi/2) + isin(pi/2)) = 12isin(pi/2) = 12i$

This is due to application of Euler's formula : $e^{i θ} = cos θ + i sin θ = c i s θ$ $e^(itheta)=costheta+isintheta =cistheta$

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What is the trigonometric form of $12 e^{\frac{π}{2} i}$ $12 e^( ( pi)/2 i )$ ?

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What is the trigonometric form of 12eπ2i12 e^( ( pi)/2 i ) ?

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What is the trigonometric form of $12 e^{\frac{π}{2} i}$ $12 e^( ( pi)/2 i )$ ?