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## Homework Statement

a) The complex number ## 1-i ## is denoted by ##u##. On an argand diagram, sketch the loci representing the complex numbers ## z## satisfying the equations ## |z-u|= |z| and |z-i|=2 ##

b) Find the argument of the complex numbers represented by the points of intersection of the two loci above.

## Homework Equations

## The Attempt at a Solution

a)The points on the argand diagram are ## (1,-i), (0,i)## now for ## |z-u|= |z| ##, the textbook indicates that we join point## (1,-i) ## to the origin and draw a bisector of the line segment,

**why**? for point ## (0,i),## this point will have a radius of 2 units and the loci will be a circle, for this one i understand.

b)Now the points of intersection seem to be the point ## (2,i)## which gives an angle of ##θ=26.56^0 ## which is correct, and the other intersection point will give ## θ= 270^0 ## or ##-0.5Π##, i don't understand how the second argument of ## θ= 270^0## is found. regards