Question

what will be the perimeter of the locus represented by arg(z+i/z-i)=Pie/4 where i=(-1)^(1/2)

Answer 1

are u sure that the question is correct?

Answer 2

arg(z+i/z-i) = arg(z+i) -arg(z-i) = pie/4
this doesnt give, in my opinion any defind locus

Answer 3

its actually a circular arc that subtends an angle of \[\Pi/4\] at the centre

Answer 4

I can arrive at this expression:\[x ^{2}+(y-1)^{2}=2x\] where x and y are the Re(z) and Im(z) respectivly

Answer 5

so i guess u have to find line integral of this expression, not sure about the integration limits tough