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Question

If A,B,C are angles of a triangle such that x=cisA,y=cisB,z=cisC, then find the value of xyz.

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Solution

Using Euler rormula cis(θ)=eiθ

So x=eiA,y=eiB and z=eiC

Hence xyz=eiAeiBeiC=ei(A+B+C)=ei(π) (Since A,B,C are angles of a triangle so, A+B+C=π)

=cosπ+isinπ=1+0=1

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