(A) By the triangle inequality, for any complex numbers $z_1$ and $z_2$, we have $|z_1| + |z_2| \geq |z_1 + z_2|$.Let $z_1 = z$ and $z_2 = 1 - z$.Then

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(A) By the triangle inequality, for any complex numbers $z_1$ and $z_2$, we have $|z_1| + |z_2| \geq |z_1 + z_2|$.Let $z_1 = z$ and $z_2 = 1 - z$.Then $|z| + |1 - z| \geq |z + (1 - z)|$.Since $|1 - z| = |z - 1|$, we have $|z| + |z - 1| \geq |1|$.Thus, $|z| + |z - 1| \geq 1$.The minimum value is $1$.

Class 11 Mathematics 1 Complex Numbers and Quadratic Equations: Complex Numbers Geometry of complex numbers

Medium

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

WBJEE 2019 All WBJEE

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

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1 Complex Numbers and Quadratic Equations: Complex Numbers

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Geometry of complex numbers

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

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