Question

If $Re\left[\frac{z+4}{2z-i}\right]=\frac{1}{2}$ then z is represented by a point lying on

• A. a circle
• B. an ellipse
• C. a straight line
• D. none of these

Answer 1

The correct option is C a straight line

Substitute $z=x+iy$
$Re\left[\frac{z+4}{2z-i}\right]=Re\left[\frac{(x+iy)+4}{2(x+iy)-i}\right]=\frac{1}{2}$
$\frac{2x^2+5x+2y^2-y}{4x^2+4y^2-4y+1}=\frac{1}{2}$
$\Rightarrow 10x+2y=1$