Question

give the solution of this question

Answer 1

$\frac{\sqrt{2} + i}{\sqrt{2} - i}$

$\frac{\sqrt{2} + i}{\sqrt{2}-i} \times \frac{\sqrt{2}+i}{\sqrt{2}+i}$

$\frac{(\sqrt{2}+i)^2}{(\sqrt{2})^2-i^2}$

$\frac{2+ 2\sqrt{2}i + i^2}{2-(-1)} \Rightarrow \frac{2+2\sqrt2i-1}{2+1}$

$\frac{1+2\sqrt2i}{3} \Rightarrow \frac{1}{3} + i\frac{2\sqrt2}{3}$

$\text{Real part : } \frac{1}{3} \text{ and, imaginary part : } \frac{2\sqrt2}{3}$

$\text{Modulus of complex number : } \sqrt{Re(i)^2+Im(i)^2}$

$\sqrt{(\frac{1}{3})^2+(\frac{2\sqrt2}{3})^2}$

$\sqrt{\frac{1}{9}+\frac{8}{9}}$

$\sqrt{\frac{1+8}{9}}$

$\sqrt{\frac{\cancel{9}}{\cancel{9}}}$

$\sqrt{1}$

$1$

Answer 2

option c is correct