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Question

If z lies on the curve arg(z+i)=π4, then minimum value of |z+43i|+|z4+3i| is

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Solution

Letz=x+iyarg(x+i(y+1))=Π4tan1y+1x=Π4y+1x=1=>x=y+1xy=1

assume x=1; y=0 (minimun value)

Therefore z=1=|z+43i|+|z4+3i|=|1+43i|+|14+3i|=|53i|+|3+3i|=9+9+9+9=218=>72


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