Q96 / 155 · WBJEE 2019 · Mathematics

For any non-zero complex number $z$, the minimum value of $|z|+|z-1|$ is

Correct answer
A
1
B
$\frac{1}{2}$
C
0
D
$\frac{3}{2}$

Solution

$|z|+|z-1| a$ is complex number $$ \begin{array}{c} |z|+|-(1-z)| \quad|a|=|-a| \\ |z|+|1-z| \quad\{\because|a|=|-a|\} \\ |z|+|1-z| \geq|z+1-z| \\ |z|+|1-z| \geq|1| \\ |z|+|1-z| \geq 1 \\ |z|+|-(z-1)| \geq 1 \\ |z|+|z-1| \geq 1 \end{array} $$ Minimum value of $|z|+|z-1|=1$

Hence, the correct answer is option: 'A'.

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