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Complex Numbers and Quadratic Equations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers and Quadratic Equations1 Mark
MCQ
If $z = 3 + 5i,$ then $z^3+ z + 198 =$
  • A
    $3 - 15i$
  • B
    $-3 - 15i$
  • C
    $-3 + 15i$
  • ✓
    $3 + 15i$
✓

Answer

Correct option: D.
$3 + 15i$
$ z=3+5 i $
$ z^3=(3+5 i)^3$
$ =3^3+3.3^2(5 i)+3.3(5 i)^2+(5 i)^3 $
$ =27-125 i+135 i-225 $
$ =-225+27+(135-125) i $
$ =-198+10 i $
$ \therefore z^3+z+198 $
$ =-198+10 i+3+5 i+198 $
$ =3+15 i $

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