Question

Find the value of $\frac{13}{3-\sqrt{10}i}$ given that $i=\sqrt{-1}$.

• A. $\frac{39+13\sqrt{10}i}{19}$
• B. $3-\frac{\sqrt{10}}{13}i$
• C. $\frac{3-\sqrt{10}i}{13}$
• D. $26-13\sqrt{10}i$

Answer 1

The correct option is A $\frac{39+13\sqrt{10}i}{19}$

$\frac{13}{3-\sqrt{10}i}=\frac{13}{3-\sqrt{10}i}\times \frac{3+\sqrt{10}i}{3+\sqrt{10}i}$

$=\frac{39+13\sqrt{10}i}{(3-\sqrt{10}i)\times (3+\sqrt{10}i)}$

$=\frac{39+13\sqrt{10}i}{9+10}$

$=\frac{39+13\sqrt{10}i}{19}$