Question

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

Answer 1

given $\frac{5+\sqrt{2}i}{1-\sqrt{2}i}$

rationalizing the denominator we get

$\frac{5+\sqrt{2}i(1+\sqrt{2}i)}{1-\sqrt{2}i(1+\sqrt{2}i)}=\frac{5-2+6\sqrt{2}i}{3}=1+2\sqrt{2}i$

therefore $a=1.b=2\sqrt{2}$