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STD 11 - 4.1 complex nubers — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 4.1 complex nubers1 Mark
MCQ
If ${z_1} = (4,5)$ and ${z_2} = ( - 3,2)$then $\frac{{{z_1}}}{{{z_2}}}$ equals
  • A
    $\left( {\frac{{ - 23}}{{12}},\frac{{ - 2}}{{13}}} \right)$
  • B
    $\left( {\frac{2}{{13}},\frac{{ - 23}}{{13}}} \right)$
  • ✓
    $\left( {\frac{{ - 2}}{{13}},\frac{{ - 23}}{{13}}} \right)$
  • D
    $\left( {\frac{{ - 2}}{{13}},\frac{{23}}{{13}}} \right)$
✓

Answer

Correct option: C.
$\left( {\frac{{ - 2}}{{13}},\frac{{ - 23}}{{13}}} \right)$
c
(c) $\frac{{{z_1}}}{{{z_2}}} = \frac{{4 + 5i}}{{ - 3 + 2i}} \times \frac{{ - 3 - 2i}}{{ - 3 - 2i}}$$ = \frac{{ - 12 - 8i - 15i + 10}}{{9 - {{(2i)}^2}}}$
$\frac{{{z_1}}}{{{z_2}}} = \frac{{ - 2}}{{13}} - i\left( {\frac{{23}}{{13}}} \right) = \left( {\frac{{ - 2}}{{13}},\frac{{ - 23}}{{13}}} \right)$

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