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COMEDK2023MathematicsComplex Number

If i= -1 and n is a positive integer, then i^n+i^ n+1 +i^ n+2 +i^ n+3 is equal to

Options

  1. A1
  2. Bi
  3. Ci^n
  4. D0

Correct answer

D. 0

Step-by-step solution

aligned Given, i^n+ & i^ n+1 +i^ n+2 +i^ n+3 =i^n (1+i+i^2+i^3 ) & =i^n (1+i+(-1)+ (i^2 ) i ) & =i^n(1+i+(-1)+(-1) i) & =i^n[(1+i)-(1+i)]=i^n(0)=0 aligned

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