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AP EAMCET2002MathematicsComplex Number

If z=3+5 i , then z^3+ z +198 is equal to

Options

  1. A-3-5 i
  2. B-3+5 i
  3. C3-5 i
  4. D3+5 i

Correct answer

D. 3+5 i

Step-by-step solution

We have, aligned z & =3+5 i z & =3-5 i z^3 & =z^2 z=(3+5 i)^2(3+5 i) & =(9-25+30 i)(3+5 i) & =(-16+30 i)(3+5 i) & =-48-150+10 i & =-198+10 i aligned Now, aligned z^3+ z +198 & =-198+10 i +3-5 i+198 & =3+5 i aligned

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