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Math Help - Help for Complex Numbers Questions

  1. #1
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    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!




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  2. #2
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    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 \\ \\<br /> <br />
\text{Divide by 3:} & x^2 - 2x + y^2 &=&0 \\ \\<br /> <br />
\text{Complete the square:} & x^2 - 2x \:{\color{red}+\: 1} + y^2 &=&0\: {\color{red}\:+\: 1} \\ \\<br /> <br />
\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.
    .
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