Q. 26 C4.0( 4 Votes )

State True of False for the following:

For any complex number z the minimum value of |z| + |z – 1| is 1.

Answer :

True

Explanation:


Given |z| + |z – 1|


We know that |z1| + |z2| ≥ |z1 – z2|


|z| + |z – 1| ≥ |z – (z – 1) |


|z| + |z – 1| ≥ 1


So, minimum value of |z| + |z – 1| is 1.


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