The resultant complex number when $(4 + 6 i)$ is divided by $(10 - 5 i)$ is

\frac{2}{25} + \frac{16}{25} i

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\frac{2}{25} - \frac{16}{25} i

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\frac{2}{5} + \frac{6}{5} i

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\frac{2}{5} - \frac{6}{5} i

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Solution

The correct option is A $\frac{2}{25} + \frac{16}{25} i$
The value of $\frac{4 + 6 i}{10 - 5 i}$
$= \frac{4 + 6 i}{10 - 5 i} \times \frac{10 + 5 i}{10 + 5 i}$
$= \frac{(4 + 6 i) (10 + 5 i)}{(10 - 5 i) (10 + 5 i)}$
$= \frac{40 + 20 i + 60 i - 30}{100 + 25}$
$= \frac{10 + 80 i}{125}$
$= \frac{2}{25} + \frac{16}{25} i$

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