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Math Help - complex number locus

  1. #1
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    complex number locus

    i really need help on this...
    if z is an imaginary number, and a is a real parameter, sketch the locus of;
    z-5 = ai(z+5)
    i know how it would work if it were moduli, but not a clue with just the imaginary numbers as they are
    help please!
    thanks
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by allazkatraz View Post
    i really need help on this...
    if z is an imaginary number, and a is a real parameter, sketch the locus of;
    z-5 = ai(z+5)
    i know how it would work if it were moduli, but not a clue with just the imaginary numbers as they are
    help please!
    thanks
    Write z=x+iy
    And substitute in the equation.

    x and y will be the coordinates of z in the complex plane, so an equation between the two will give you the locus
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  3. #3
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    re:

    ok, i understand that part, but then i get to this point;

    y= [10+x(ai-1)] / (a+i)

    and i don't know what to do with it..
    i know that the answer is supposed to be a circle, but how do i get rid of the a's in my equation? do i even need to?
    thanks for the help so far
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  4. #4
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    Quote Originally Posted by allazkatraz View Post
    ok, i understand that part, but then i get to this point;

    y= [10+x(ai-1)] / (a+i)

    and i don't know what to do with it..
    i know that the answer is supposed to be a circle, but how do i get rid of the a's in my equation? do i even need to?
    thanks for the help so far
    If you do what moo suggests you will get

    x + iy = -ay + i(ax + 5a).

    Equate real and imaginary parts on each side:

    x = -ay => a = -x/y .... (1)

    y = ax + 5a = a(x + 5) .... (2)

    Substitute (1) into (2) etc.
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