If {z₁} = (4,5) and {z₂} = ( - 3,2) then frac{{{z₁}}}{{{z₂}}} equals

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4-1.Complex numbers

easy

If ${z_1} = (4,5)$ and ${z_2} = ( - 3,2)$then $\frac{{{z_1}}}{{{z_2}}}$ equals

$\left( {\frac{{ - 23}}{{12}},\frac{{ - 2}}{{13}}} \right)$

$\left( {\frac{2}{{13}},\frac{{ - 23}}{{13}}} \right)$

$\left( {\frac{{ - 2}}{{13}},\frac{{ - 23}}{{13}}} \right)$

$\left( {\frac{{ - 2}}{{13}},\frac{{23}}{{13}}} \right)$

Solution

(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}}}$
$\frac{{{z_1}}}{{{z_2}}} = \frac{{ – 2}}{{13}} – i\left( {\frac{{23}}{{13}}} \right) = \left( {\frac{{ – 2}}{{13}},\frac{{ – 23}}{{13}}} \right)$

Standard 11

Mathematics

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