What is the trigonometric form of $5 e^{\frac{3 π}{2} i}$ $5e^( (3pi)/2 i )$ ?

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Answer 1 · 2018-03-05T14:13:39

See the explanation below

Apply Euler's Identity

$e^{i θ} = cos θ + i sin θ$ $e^(itheta)=costheta+isintheta$

Therefore,

The trigononetric form is

$z = 5 e^{\frac{3}{2} π i} = 5 (cos (\frac{3}{2} π) + i sin (\frac{3}{2} π))$ $z=5e^(3/2pii)=5(cos(3/2pi)+isin(3/2pi))$

$= 5 (0 - i)$ $=5(0-i)$

$= - 5 i$ $=-5i$

And upon simplification

$z = - 5 i$ $z=-5i$

What is the trigonometric form of 5e3π2i5e^( (3pi)/2 i ) ?