Question

If $\frac{2+3i}{(7-i)4+2i}=A+iB$ then $A^2+B^2=$?

Answer 1

Given,

$\frac{2+3i}{(7-i)4+2i}=A+iB$

$\frac{2+3i}{28-2i}=A+iB$

$\frac{2+3i}{28-2i}\times \frac{28+2i}{28+2i}$

$=\frac{50+i88}{788}$

$\therefore A+iB=\frac{25}{394}+i\frac{22}{197}$

$A^2+B^2={\left(\frac{25}{394}\right)}^2+{\left(\frac{22}{197}\right)}^2$

$\therefore A^2+B^2=\frac{13}{788}$