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Question

Find the amplitude of the complex number sin(6π/5) + i (1- cos(6π/5))

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Solution

We have sin 6π/5 + i(1 – cos 6π/5) = 2 sin 3π/5 cos 3π/5 + i(2 sin^2 3π/5) (:-sin(2∅)=2 sin∅ cos∅ And 1-cos(2∅) =2sin^2 ∅)

= 2 sin 3π/5 (cos 3π/5 + isin 3π/5)

Comparing with r(cosθ + isinθ) ,

Amplitude = θ = 3π/5 = 108º. [Ans.]


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