Complex Numbers Argand Q (1 Viewer)

[pixiefeathers]

Hello,

For this question,


I know how to correctly sketch the locus but I don't know how to find its point of intersection with the Imaginary axis (which this question needs you to label). I am somewhat aware that you need to first find the centre and radius of the circle that the locus is a part of, how do you do that? Thanks

 

[gazzaboy]

You should have a major arc of a circle with the ends at 1 and -1.

To find the centre, you want to make use of the theorem "the angle at the centre is twice the angle at the circumference". So that means the angle subtended at the centre is pi/2. Use that and a bit of trigonometry to find that the radius is sqrt(2) and the centre is i.

Now that you know the radius is sqrt(2), you can deduce that the intersection point with the imaginary axis is 1 + sqrt(2).