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Question

Find the value of 1+i2+i4+i6+...+i2n where i=1,nN

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Solution

1+i2+i4+i6+...+i2n=11+11+...(1)n

Case I:If n is odd
1+i2+i4+i6+...+i2n=11+11+...+11=0

Case II:If n is even
1+i2+i4+i6+...+i2n=11+11+...+1=1

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