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AP EAMCET20228 Jul 2022Evening ShiftMathematicsComplex NumberActual

A complex number z among the following which satisfy z^3+27 i=0 is

Options

  1. A(3 3 -3 i) / 2
  2. B-3 i
  3. C(3 3 +3 i) / 2
  4. D(-3 3 +3 i) / 2

Correct answer

A. (3 3 -3 i) / 2

Step-by-step solution

Given, z^3+27 i=0 aligned & z^3-(3 i)^3=0 & (z-3 i) (z^2+3 z i-9 )=0 aligned If z-3 i=0 z=3 i If z^2+3 z i-9=0 aligned & z= -3 i -9+36 2 = -3 i 3 3 2 & z= 3 3 -3 i 2 , -3 3 -3 i 2 aligned

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