locus question (1 Viewer)

[newnoise]

w= (z-i)/(z-2)

w is purely imaginary

i keep getting a circle with radius 1 and centre 1,0

 

[gurmies]

 

[h3ll h0und]

W= z-i / z-2
If w is imaginary w=+- ni
argw = arg (z-i/z-2)
therefore,
+- pi/2 = arg (z-i) - arg (z-2)

which is a circle with radius sqrt5/2 and centre (1,1/2)