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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
If $x = 3 + i$, then $x^3 - 3x^2 - 8x + 15 = $
  • A
    $6$
  • B
    $10$
  • C
    $-18$
  • ✓
    $-15$
✓

Answer

Correct option: D.
$-15$
d
(d) $x = 3 + i\, \Rightarrow \,\,x - 3 = i\,$
$ \Rightarrow $ $\,x^2 - 6x + 10 = 0$ ==> $x^3 - 3x^2 - 8x + 15$
$ = x(x^2 - 6x + 10) + 3\,(x^2 - 6x + 10) - 15$
$ = x(0) + 3(0) - 15 = - 15$.

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