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TS EAMCET20249 May 2024Evening ShiftMathematicsComplex NumberActual

If z=1- 3 i , then z^3-3 z^2+3 z=

Options

  1. A0
  2. B1+3 3 i
  3. C1
  4. D2+3 3 i

Correct answer

B. 1+3 3 i

Step-by-step solution

Given, z=1- 3 i aligned & z^2=1+3 i^2-2 3 i=-2(1+ 3 i) & z^3=-2(1+ 3 i)(1- 3 i)=-8 aligned Now, z^3-3 z^2+3 z=-8+6+6 3 i+3-3 3 i=1+3 3 i .

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