Originally Posted by

**afeasfaerw23231233** p293 q15c

question: Suppose that $\displaystyle arg \frac {z-1}{z+1} =\frac {\pi}4 $where z is a complex no.

(a) let z = x + yi , where x and y are real. Show that the locus of z is an arc of a circle.

(b) Find the radius and centre of the circle found in (a)

(c) Find the farthest point from the origin on the locus

i've done (a)(b) correctly but don't know how to do (c).

My working:

(a)$\displaystyle \frac {x-1+yi}{x+1+yi}$

$\displaystyle = \frac {x^2 +y^2-1+2yi} {x^2+y^2 +2x+1}$

$\displaystyle \frac{2y}{x^2+y^2-1} = tan \frac{\pi} 4 = 1$

$\displaystyle x^2+y ^2-2y-1=0$

b) centre=(0,-1) radius = $\displaystyle \sqrt 2$

don't know how to do (c). Thanks.