# Math Help - Help for Complex Numbers Questions

1. ## Help for Complex Numbers Questions

Hey all, I have two problems that I'm having problems with, and it would be great if any of you could help. Thanks! I tried to copy my workings from the word document, however it didn't work, so I'm attaching the document with the 2 questions and my workings on it. All help would be appreciated, thank you!

2. Hello, somethingsmells!

Your work for the first problem is excellent!
. . Now you need to identify the graph of your equation.

$\begin{array}{cccc}\text{You have:} & 3x^2 + 3y^2 - 6x &=&0 \\ \\

\text{Divide by 3:} & x^2 - 2x + y^2 &=&0 \\ \\

\text{Complete the square:} & x^2 - 2x \:{\color{red}+\: 1} + y^2 &=&0\: {\color{red}\:+\: 1} \\ \\

\text{Factor:} & (x - 1)^2 + y^2 &=& 1 \end{array}$

We have a circle with center (1, 0) and radius 1.

The locus of a point whose distances from two fixed points
. . is a fixed ratio is called the Circle of Apollonius.
.