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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
If $x=3+ i$, then $x^3-3 x^2-8 x+15=$
  • A
    6
  • B
    10
  • C
    $-18$
  • ✓
    $-15$
✓

Answer

Correct option: D.
$-15$
(D)
$x-3+ i$
$\Rightarrow(x-3)^2= i ^2$
$\Rightarrow x^2-6 x+10=0$ ...(i)
$\therefore \quad x^3-3 x^2-8 x+15$
$=\left(x^2-6 x+10\right)(x+3)-15$
$=0(x+3)-15 \quad \ldots[From (i)]$ 
$=-15$

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