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Question

Find the conjugates of the following complex number : (1+i)2n+1(1i)2n1,nϵN

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Solution

(1+i)2n+1(1i)2n1=(1+i1i)2n1(1+i)2
=2i((1+i)2(1+i)(1i))2n1
=2i(i2n1)
=2i2n
=2(1)n
Thus, the conjugate =2(1)n

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