If z is a complex number- then the minimum value of - z - z -1- isA- 1-2B- 1C- 0D- None of these

First note that | z |= | z | and | z_1+z_2 |≤ | z_1 |+| z_2| Now | z |+ | z 1 |= | z |+ | z 1 |≥ | z+(1 z) |= | 1 |=1 Hence, minimum value of | z |+ ...

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Standard XII

Mathematics

Purely Real

If z is a com...

Question

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

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None of these

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Solution

The correct option is A 1
First note that $| - z | = | z | a n d | z_{1} + z_{2} | \leq | z_{1} | + | z_{2} |$
Now $| z | + | z - 1 | = | z | + | z - 1 | \geq | z + (1 - z) | = | 1 | = 1$
Hence, minimum value of $| z | + | z - 1 |$ is 1.

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

The correct option is A 1First note that |−z|=|z| and |z1+z2|≤|z1|+|z2| Now |z|+|z−1|=|z|+|z−1|≥|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

The correct option is A 1
First note that $| - z | = | z | a n d | z_{1} + z_{2} | \leq | z_{1} | + | z_{2} |$
Now $| z | + | z - 1 | = | z | + | z - 1 | \geq | z + (1 - z) | = | 1 | = 1$
Hence, minimum value of $| z | + | z - 1 |$ is 1.