NDA2021MathematicsComplex NumberActual

What is _ n=1 ^ 8 n+7 i^n equal to, where i= -1 ?

Options

Correct answer

A. -1

Step-by-step solution

i+i^2+i^3+i^4=i-1-i+1=0 So value of sum of each concecutive 4 pair is zero. aligned & 8 n+7=8 n+4+3=4(2 n+1)+3 & _ n=1 ^ 8 n+7 i^n=i^ 4(2 n+1)+1 +i^ 4(2 n+1)+2 +i^ 4(2 n+1)+3 & =i^ 4(2 n+1) [i+i^2+i^3 ]=1[i-1-i]=-1 aligned

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