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# Locus Of Complex Numbers watch

1. This question is for Edexcel FP2 Complex Numbers

QUESTION

P represents complex number z where

|z - 6 + 3i| = 3|z + 2 -i|

a) Show that the locus of P is a circle and find center and radius.

Q represents complex number z where
tan[arg(z+6)] = 1/2

b) Sketch locus of P and locus of Q on Argand diagram

c) shade for some inequalities ...

Attempt

I have no given solutions to these questions however I believe part a) is correct

a) I find the Cartesian equation of the circle to be (x+3)^2 + (y-3/2)^2 = 45/4

b) this is where I become uncertain. When sketching this on an argand diagram would I simply label the angle as arctan(1/2) or would it be better to label it as a rounded numerical value. (or am I missing a better method)

Also I find it difficult to know where each of the loci lie relative to each other, is it worth solving these to find points of intersection, how important is the accuracy of these diagrams for the exam.

Thank you for any pointers.
2. (Original post by Mav1)
This question is for Edexcel FP2 Complex Numbers

QUESTION

P represents complex number z where

|z - 6 + 3i| = 3|z + 2 -i|

a) Show that the locus of P is a circle and find center and radius.

Q represents complex number z where
tan[arg(z+6)] = 1/2

b) Sketch locus of P and locus of Q on Argand diagram

c) shade for some inequalities ...

Attempt

I have no given solutions to these questions however I believe part a) is correct

a) I find the Cartesian equation of the circle to be (x+3)^2 + (y-3/2)^2 = 45/4

b) this is where I become uncertain. When sketching this on an argand diagram would I simply label the angle as arctan(1/2) or would it be better to label it as a rounded numerical value. (or am I missing a better method)

Also I find it difficult to know where each of the loci lie relative to each other, is it worth solving these to find points of intersection, how important is the accuracy of these diagrams for the exam.

Thank you for any pointers.
arctan 1/2 is better
I always draw very accurate diagrams
(usually I work in Cartesian)

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Updated: February 22, 2016
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