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Algebra

find minimum value of

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

Profile image of Nilesh Joshi
15 Years agoGrade
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3 Answers

Profile image of SAGAR SINGH - IIT DELHI
15 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
Profile image of sdf
9 Years ago
please give answer
Profile image of mycroft holmes
9 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