Express the following complex numbers in the standard from $a+ib$ :

$\dfrac{5+\sqrt{2}i}{1-\sqrt{2}i}$

$\dfrac{5+\sqrt{2}i}{1-\sqrt{2}i}$

Rationalizing the denominator, we get

$= \dfrac{5+\sqrt{2}i}{1-\sqrt{2}i} \times \dfrac{1+\sqrt{2}i}{1+\sqrt{2}i}$

$= \dfrac{5+2i^2+(5+1)\sqrt{2}i}{1+2}$

$= \dfrac{3+6\sqrt{2}i}{1+2}$......................$(\because i^2=-1)$

$= 1+2\sqrt{2}i$