Maths · Modulus and argument (or amplitude) of a complex number
Calculate all solutions of
Calculate all solutions of \( |z-1| \times \mid z- \) \( \mathbf{1} \mid=\mathbf{1} \)
- A. intersecting straight line passing through (1,0)
- B. solutions are exactly the points of the circle with center (1,0) and radius 1
- C. solutions are exactly the points of the circle with center (1,0) and radius \( \sqrt{2} \)
- D. none of these
Step-by-step solution
The equation is |z-1| * |z-1| = 1, which simplifies to |z-1|^2 = 1, so |z-1| = 1. This represents a circle in the complex plane with center at (1,0) and radius 1.