You are Here: Home >< Maths

FP1 further maths complex numbers question watch

Another question, if we are given that |z-2-2i|=2 and arg(z-2-2i)=pi/6 how do we find the value for z in the form a+ib? Thanks.
Just draw the circle, draw on the line of the argument from the centre of the circle, then work out the point of intersection between the two using Pythagoras. You can deduce the general formula in these situations yourself.
2. Also, how would I solve the question: 'for the transformation w=z-1+2i sketch on separate Argand diagrams the locus of w when:

c) z lies on the line with equation y=2x+1

-> why does it cross at (-2, 0) and (0, 4)?? as these do not fit the equation y=2x+1...

??
Also, how would I solve the question: 'for the transformation w=z-1+2i sketch on separate Argand diagrams the locus of w when:

c) z lies on the line with equation y=2x+1

-> why does it cross at (-2, 0) and (0, 4)?? as these do not fit the equation y=2x+1...

??
It doesn't have to cross those coords since you're TRANSFORMING that eq, so coords in the uv-plane wont work on the eq in the xy-plane. That said, are you sure those are the coordinates...? Following the procedure we get something slightly different.

Say and
Then we have thus and . So, if our line crosses at on the xy plane, then it must cross and on the uv plane.

Anywho, you simply need to sub in and into the equation , and simplify to get an equation in . However, while it satisfies the conditions we deduced above, it does not satisfy those points that you said.

Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 15, 2017
Today on TSR

Top unis in Clearing

Tons of places at all these high-ranking unis

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants