Question

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

• A. $\frac{2}{25}+\frac{16}{25}i$
• B. $\frac{2}{25}-\frac{16}{25}i$
• C. $\frac{2}{5}+\frac{6}{5}i$
• D. $\frac{2}{5}-\frac{6}{5}i$

Answer 1

The correct option is A $\frac{2}{25}+\frac{16}{25}i$

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

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

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

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

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

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