The region of the z plane for which $|\frac{z-a}{z+a}|=1 (Re~a \ne 0)$ is
- A. x-axis
- B. y-axis
- C. The straight line $z=|a|$
- D. None of the above
Answer: B. y-axis
Explanation: $|\frac{z-a}{z+a}| = 1 \Rightarrow |z-a| = |z+a| \Rightarrow |x+jy-a| = |x+jy+a| \Rightarrow (x-a)^2+y² = (x+a)^2+y² \Rightarrow x²+a²-2ax+y² = x²+a²+2ax+y² \Rightarrow 4ax = 0 \Rightarrow x = 0$. The equation $x = 0$ corresponds to the y-axis.