Question

If $\alpha$ and $\beta$ are real then $\left|\frac{\alpha +i\beta }{\beta +i\alpha }\right|=$

• A. Lies betwen 0 and 1
• B. = 1
• C. >1
• D. 2

Answer 1

The correct option is B = 1

We know that
$|\frac{z_1}{z_2}|$ $=\frac{|z_1|}{|z_2|}$
Hence
$|\frac{\alpha +i\beta }{\beta +i\alpha }|$
$=\frac{|\alpha +i\beta |}{|\beta +i\alpha |}$
$=\frac{\sqrt{{\alpha }^2+{\beta }^2}}{\sqrt{{\beta }^2+{\alpha }^2}}$
$=1$.