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AP EAMCET20225 Jul 2022Morning ShiftMathematicsComplex NumberActual

By simplifying i¹⁸-3 i^7+i^2 (1+i^4 )(i)²² , we get

Options

  1. A-1+3 i
  2. B1-3 i
  3. C1+3 i
  4. D-1-3 i

Correct answer

C. 1+3 i

Step-by-step solution

i¹⁸-3 i^7+i^2 (1+i^4 )(i)²²=i^ 4 4+2 -3 i⁴⁺³+-1(1+1) (i^2 )¹¹=i^2-3 i^3+2 [ i^2=-1 . and .i^4=1 ]=-1+3 i+2=1+3 i

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