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find minimum value of mod(2z-1) + mod(3z-2)

find minimum value of


mod(2z-1) + mod(3z-2)

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3 Answers

SAGAR SINGH - IIT DELHI
879 Points
11 years ago
Dear student,
mod(2z-1)=mod(2x-1+i2y)<root(4x2+-4x+4y2)
mod(3z-2)=mod(3x-2+i3y)< root(9x2+4-12x+9y2)
nowfind the minimum value easily....
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Askiitians Expert
Sagar Singh
B.Tech, IIT Delhi
sdf
11 Points
5 years ago
please give answer
mycroft holmes
272 Points
5 years ago
2|z-1/2|+3|z-2/3| = 2[ |z-1/2|+|2/3 – z| ] + |z-2/3]
By triangle inequality we have that the expression
\ge 2 \left|\frac{2}{3} - \frac{1}{2} \right| + \left|z -\frac{2}{3} \right|
\ge \frac{1}{3} + \left|z -\frac{2}{3} \right|
Equality occurs when z = 2/3
Hence min is 2/3

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