Maths · Modulus and argument (or amplitude) of a complex number
For a complex number z, the minimum value of is
For a complex number z, the minimum value of \( |z|+|z-2| \) is
- A. 1
- B. 2
- C. 3 \)
- D. None of these
Step-by-step solution
The expression |z|+|z-2| represents the sum of distances from z to 0 and to 2 on the real axis. By the triangle inequality, the minimum occurs when z lies on the line segment connecting 0 and 2, giving a sum equal to the distance between 0 and 2, which is 2.