Question

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

• A. $2i$
• B. $2$
• C. $-2i$
• D. $-2$

Answer 1

The correct option is C $-2i$

Given,

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

Now,$\sqrt{3+4i}=\sqrt{4+4i+i^2}=\sqrt{{(2+i)}^2}=2+i$

Similarly, $\sqrt{3-4i}=2-i$

$\Rightarrow =\frac{2+i+2-i}{2+i-(2-i)}$

$=\frac{4}{2i}$

$=\frac{2}{i}=-2i$