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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
If ${(\sqrt 8 + i)^{50}} = {3^{49}}(a + ib)$ then ${a^2} + {b^2}$ is
  • A
    $3$
  • B
    $8$
  • ✓
    $9$
  • D
    $\sqrt 8 $
✓

Answer

Correct option: C.
$9$
c
(c) ${(\sqrt 8 + i)^{50}} = {3^{49}}(a + ib)$
Taking modulus and squaring on both sides, we get
${(8 + 1)^{50}} = {3^{98}}({a^2} + {b^2})$
${9^{50}} = {3^{98}}({a^2} + {b^2})$
${3^{100}} = {3^{98}}({a^2} + {b^2})$
==> $({a^2} + {b^2}) = 9$.

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