Answer to Question #141166 in Complex Analysis for Sanamtha

Question

Solve the equation 13z/z+1 = 11-3i zeC [where C denotes the set of complex numbers]

Answer 1

Let $z=x+iy.$

$13x+13iy=(x+iy+1)(11-3i);$

$13x+13iy=11x+11iy+11-3ix+3y-3i;$

$2x-3y+i(3x+2y)=11-3i;$

$\begin{cases} 2x-3y=11, \\ 3x+2y=-3; \end{cases}$

$\begin{cases} x=\frac{11+3y}{2},\\ \frac32(11+3y)+2y=-3; \end{cases}$

$16.5+4.5y+2y=-3;$

$6.5y=-19.5;$

$y=-3;$

$x=1.$

$z=1-3i.$