Topic: Electronics Engineering
Consider the equation $Re(1/z)=c,$ where z is a complex number, c is a nonzero constant and Re() represents the real part. The equation describes a
- A. Straight line
- B. Parabola
- C. Circle
- D. None of these
Answer: C. Circle
Explanation: $\frac{1}{Z}=\frac{1}{x+iy}\frac{x-iy}{x-iy}=\frac{x-iy}{x^{2}+y^{2}}$. $Re\{\frac{1}{z}\}=\frac{x}{x^{2}+y^{2}}=c$. $x^{2}+y^{2}=\frac{x}{c} \Rightarrow x^{2}+y^{2}-\frac{x}{c}=0$. This is the equation of a circle.