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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 $z = 2 - 3i$ then $z^2 - 4z + 13 =$
  • ✓
    $0$
  • B
    $1$
  • C
    $2$
  • D
    $3$
✓

Answer

Correct option: A.
$0$
$z = 2 - 3i$
$z^2 = 2^2 - 3^2 - 12i$
$= -5 - 12i$
$\therefore z^2 - 4z + 13$
$= (-5 - 12i) - 4(2 - 3i) + 13$
$= -5 - 12i - 8 + 12i + 13$
$= -13 + 13$
$= 0$

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