If {z_1} = (4,5) and {z_2} = (-3,2),then frac | vedclass

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(C) Given ${z_1} = 4 + 5i$ and ${z_2} = -3 + 2i$. To find $\frac{z_1}{z_2}$,we multiply the numerator and denominator by the conjugate of the denomina

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

Vedclass · Answer

(C) Given ${z_1} = 4 + 5i$ and ${z_2} = -3 + 2i$. To find $\frac{z_1}{z_2}$,we multiply the numerator and denominator by the conjugate of the denominator: $\frac{z_1}{z_2} = \frac{4 + 5i}{-3 + 2i} 	imes \frac{-3 - 2i}{-3 - 2i}$ $= \frac{-12 - 8i - 15i - 10i^2}{(-3)^2 - (2i)^2}$ $= \frac{-12 - 23i + 10}{9 + 4}$ $= \frac{-2 - 23i}{13}$ $= \frac{-2}{13} - i\left( \frac{23}{13} ight)$ In coordinate form,this is $\left( \frac{-2}{13}, \frac{-23}{13} ight)$.

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

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