Question

Solve $\frac{\sqrt{3+4ı}+\sqrt{3-4ı}}{=\sqrt{3+4ı}-\sqrt{3-4ı}}$

Answer 1

$\frac{\sqrt{3+4i}+\sqrt{3-4i}}{\sqrt{3+4i}-\sqrt{3-4i}}$

$=\frac{\sqrt{3+4i}+\sqrt{3-4i}}{\sqrt{3+4i}-\sqrt{3-4i}}\times \frac{\sqrt{3+4i}+\sqrt{3-4i}}{\sqrt{3+4i}+\sqrt{3-4i}}$

$=\frac{3+4i+3-4i+2\sqrt{9+16}}{3+4i-3+4i}$

$=\frac{6+2\sqrt{25}}{4i}$

$=\frac{6+10}{4i}$

$=\frac{16}{4i}\times \frac{i}{i}$

$=-4i$ since $i^2=-1$