Complex numbers locus (1 Viewer)

[ColdBuffet]

Hi, could someone help me with this question please.

Draw a sketch and describe the locus of z given by the equation arg(z-1) - arg (z+i) = pie/4, noting any exclusions.

I'm not sure how to find the centre and radius when the two points are on different axes. I know the angle pie/4 is above the x axes but how do you know whether it is in the first or second quadrant?

Thanks.

 

[tommykins]

start with open circle at point (0,-1) and go ANTI CLOCKWISE to the point (1,0) and the angle from the 2 points to the circumerfence is pi/4.