Question

If $z\in C$, the minimum value of $|z|+|z-5|$ is attained by

• A. $z=0$
• B. $z=5$
• C. $z=5/2$
• D. For all $z\in [0,5]$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $z=5$
B $z=0$
C $z=5/2$
D For all $z\in [0,5]$

$|z|$ means the distance between complex number $z$ and $(0,0)$.

$|z-5|$ means the distance between $z$ and $(5,0)$.

For $|z|+|z-5|$ to be minimum , $z$ should either lie between the points $(0,0)$ and $(5,0)$ on the line joining them or on these points.

So $z\in [0,5]$

Hence $z=0$, $z=5$ and $z=\frac{5}{2}$ also satisfies the equation.