\hspace{-16} $ Minimum value of $\bf{\left|z-1-i \right| + \left |z+2-3i \right| + \left |z+3+2i \right|}$\\\\\\ where $\bf{z = x+iy}$ and $\bf{i = \sqrt{-1}}$
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1 Answers
2305Plot the points A(1,1),B(-2,3) and C(-3,-2).
We want to find P(x,y) such that PA+PB+PC is minimum.
This point P is the Fermat's point.
The unique property of the Fermat point is that,
<APB=<APC=<BPC=120°
PA = ei 120°PB
(1+i-x-iy)=(-12+√3i2)(-2+3i-x-iy)..(i)
and,
PB = ei 120°PC
(-2+3i-x-iy)=(-12+√3i2)(-3-2i-x-iy)...(ii)
Solving i and ii you'll the required point.
Anik Chatterjee i think it will be PB = ei 120°PA &PC = ei 120°PB..Upvote·0· Reply ·2013-08-05 06:09:34- Shaswata Roy My bad!!The angles will be -120 and not 120.Or we can Interchange between PA,PB and PC like you've done.
man111 singh Thanks Shaswata