1.

Ifzsatisfiesthe conditionarg(z + i)=(pi)/(4) . Then theminimumvalue of|z +1 - i| +|z - 2 +3 i| is _______.

Answer»


Solution :Locus given by equation `arg(z+i) =(pi)/(3)` is a ray EF as SHOW in the FOLLOWINGFIGURE.

COMPLEX number z moves on ray Ef.
Now,for any position of complex number P(z) on the ray EF, `|z-(-1+i)|+|z-(2-3i)|=PA+ PB`
Clearly, PA+PB is minimum when POINTP isa point C, where point A,C and B are COLLINER.
So, `(PA +PB)_("min") = AB = 5`


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