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If z is a complex number, then the minimum value of |z| + |z − 1| is ______.

+1 vote

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asked Mar 27, 2021 in Uncategorized by Doubtly (98.9k points)
reopened Jun 29, 2023 by Doubtly

jeemain
complexnumbers

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1 Answer

+1 vote

answered Mar 27, 2021 by Doubtly (98.9k points)
selected Jun 29, 2023 by Doubtly

Best answer

First, note that |-z|=|z| and |z1 + z2| ≤ |z1| + |z2|
Now |z| + |z-1| = |z| + |1 - z| ≤ |z + (1 - z)|

= |1|

= 1

Hence, minimum value of |z| + |z - 1| is 1.

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