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4-1.Complex numbers
medium
The minimum value of $|2z - 1| + |3z - 2|$is
A
$0$
B
$1/2$
C
$1/3$
D
$2/3$
Solution
(c) Given expression, $|2z – 1| + |3z – 2|$, minimum value of $|2z – 1|$is $0$ at $z = \frac{1}{2}$. So value of given expression $ = 0 + \frac{1}{2} = \frac{1}{2},$ minimum value of $|3z – 2|$ is $0$, at $z = \frac{2}{3}$. So value of given expression $ = \frac{1}{3} + 0 = \frac{1}{3}$.
So minimum value of given expression is $\frac{1}{3}$.
Standard 11
Mathematics
