SOLUTION: This is another question from a past Algebra & Complex Numbers paper which I am practicing for study for my Calculus exam. The question is apparently worth an excellence mark: Q

Question 167782: This is another question from a past Algebra & Complex Numbers paper which I am practicing for study for my Calculus exam. The question is apparently worth an excellence mark:
QUESTION EIGHT
Find the equation of the locus of the point representing z if |z-3i|-|z+3i|=2.
I can work it out as far as:
|z-3i|-|z+3i|=2
(z=x+iy) => |x+i(y-3)|-|x+i(y+3)|=2
(|z|=) => -=2
-=2
but after that I get stuck.
Help appreciated.
Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
Let take
Let take
Note that w-z = -12y
then

then

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