Question

Express $\frac{5+\sqrt{2}i}{1-\sqrt{2}i}$ in the form of $a + ib$ .

• A. $1-2 \sqrt{2}i$
• B. $1-\sqrt{2}i$
• C. $1+2\sqrt{2}i$
• D. $1+\sqrt{2}i$

Answer 1

Answer: (C)

We have, $\frac{5+\sqrt{2}i}{1-\sqrt{2}i}$
$=\frac{5+\sqrt{2}i}{1-\sqrt{2}i}\times\frac{1+\sqrt{2}i}{1+\sqrt{2}i}$
$=\frac{5+5\sqrt{2}i+\sqrt{2}i-2}{1-\left(\sqrt{2}i\right)^{2}}$
$=\frac{3\left(1+2 \sqrt{2}i\right)}{3}$
$=1+2\sqrt{2}i$