Convert the given complex number in polar form i and evaluate

Asked by Abhisek | 2 years ago |  89

1 Answer

Solution :-

The complex number is i

Let rcosθ = 0 and rsinθ = 1

Squaring and adding

\( r^2cos^2θ + r^2sin^2θ = 0^2+1^2\)

\( r^2(cos^2θ + sin^2θ) =1\)

\( r^2=1 \)

\( r=\sqrt{1}=1\)  [Conventionally, r > 0]

cosθ = 0 and sinθ = 1

\( θ =\dfrac{\pi}{2}\)

i = rcosθ + irsinθ 

\( cos\dfrac{\pi}{2}+ isin\dfrac{\pi}{2}\)

Required polar form

Answered by Pragya Singh | 2 years ago

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