The locus of the complex number Z such that $\arg \left(\frac{Z-1}{Z+1}\right)=\frac{\pi}{4}$ is

The locus of the complex number Z such that $\arg \left(\frac{Z-1}{Z+1}\right)=\frac{\pi}{4}$ is
  1. a straight line
  2. a circle
  3. a parabola
  4. an ellipse

Solution


Required locus is an arc of circle.

Asked in: AP EAMCET 2024 (22 May Shift 1)

Practice more Complex Number questions on Aicharya