complex number locus question (1 Viewer)

[jfanny123]

does anyone know how to sketch
arg(z-2)-arg(z-i)=π(pie)/2

i know it is a circle with centre (1,0.5) but i dont know if it is the semicircle above or below because i think it should be above but some textbook said it is below. can someone tell me why???
thanks realli much

 

[Amplifiedspeakr]

The locus can be upper or lower depending on where n is greater than or less than 1. If n is positive, then the locus is the upper semi circle with centre you have found and radius (root 5)/2.
If n is negative then the locus is the lower semicircle with same radius and centre.