If z is a complex number, then the minimum va | vedclass

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Question

(a)First note that $| - z|\, = \,|z|$ and $|{z_1} + {z_2}|\, \le \,|{z_1}| + |{z_2}|$
Now $|z| + |z - 1|\, = \,|z| + |1 - z|\, \ge \,|z + (1 - z)|\,

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(a)First note that $| - z|\, = \,|z|$ and $|{z_1} + {z_2}|\, \le \,|{z_1}| + |{z_2}|$
Now $|z| + |z - 1|\, = \,|z| + |1 - z|\, \ge \,|z + (1 - z)|\, = \,|1| = 1$
Hence, minimum value of $|z| + |z - 1|$is $1.$

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

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