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AP EAMCET201822 Apr 2018Evening ShiftMathematicsComplex NumberActual

If z C and i z^3+4 z^2-z+4 i=0 , then a complex root of this equation having minimum magnitude is

Options

  1. A4 i
  2. B1-i 2
  3. C3 +i 2
  4. D1+i 2

Correct answer

B. 1-i 2

Step-by-step solution

Given complex equation, array cc & i z^3+4 z^2-z+4 i=0 & z^2(i z+4)+i(i z+4)=0 & (i z+4) (z^2+i )=0 & z=4 i or z^2=i & z=4 i or & ( 1 2 - 1 2 i ) array So, the complex root having minimum magnitude is 1-i 2 or -1+i 2

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