Question

lf $(\overline{a}+\overline{b}).(\overline{a}-\overline{b})=0$ then $|\overline{a}|$: $|\overline{b}|$ is:

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $2:3$

Answer 1

The correct option is A $1:1$

Expanding
$(\overline{a}+\overline{b}).(\overline{a}-\overline{b})={\overline{a}}^2+\overline{a}.\overline{b}-\overline{b}.\overline{a}-{\overline{b}}^2$=0
$|\overline{a}{|}^2-|\overline{b}{|}^2=0$
$|\overline{a}{|}^2=|\overline{b}{|}^2$

$\frac{|\overline{a}{|}^2}{|\overline{b}{|}^2}=1$

$\frac{|\overline{a}|}{|\overline{b}|}=1$