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

The value of $\cfrac{4 + 6i}{10 - 5i}$

$= \cfrac{4 + 6i}{10 - 5i} \times \cfrac{10 + 5i}{10 + 5i}$

$= \cfrac{(4 + 6i)(10 + 5i)}{(10 - 5i)(10 + 5i)}$

$= \cfrac{40 + 20i + 60i - 30}{100 + 25}$

$= \cfrac{10 + 80i}{125}$

$= \cfrac{2}{25} + \cfrac{16}{25}i$