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

1

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\frac{1}{2}

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0

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\frac{3}{2}

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Solution

The correct option is A $1$
$| z | + | z - 1 | \geq | z - (z - 1) | \Rightarrow | z | + | z - 1 | \geq 1$
$\Rightarrow$ Minimum value of $| z | + | z - 1 | = 1$

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Similar questions

If z is a complex number, then the minimum value of $| z | + | z - 1 |$ is

z

| z | + | z - 1 |

(\bar{z})

Z_{1}

Z_{2}

(| Z_{1} | + | Z_{2} |) ∣ ∣ ∣ \frac{Z_{1}}{| Z_{1} |} + \frac{Z_{2}}{| Z_{2} |} ∣ ∣ ∣

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