Question

If z is a complex number, then find the minimum value of $\left|z\right|+|z-1|+|2z-3|.$

• A. $E=1$
• B. $E=2$
• C. $E=3$
• D. $E=4$

Answer 1

The correct option is B $E=2$

$E=\left|z\right|+|z-1|+|2z-3|=\left|z\right|+|z-1|+|3-2z|\ge |z+z-1+3-2z|=2$
$\therefore ,\left|z\right|+|z-1|+|2z-3|\ge 2$
Therefore, minimum value is 2.
Ans: B