1. Hi!
This is a problem taken from a textbook, but it's not a homework problem. I'm just rehearsing for a test.
Determine which complex numbers satisfy the equation .
You are supposed to make a geometrical interpretation, and in the key it says "the complex numbers that lie on the ellipse .
However, I don't understand how they arrive at this result. Could somebody explain, please?  2.

3. is the Euclidean distance, in the complex plane, between and Correction: not -1 but -i. Likewise, is the Euclidean distance between and . Correction: not 1 but i.

Now the locus of points such that the sum of the distances between and two given points is equal to a given constant (greater than the distance between the two points) is an ellipse.

You do the math to transform the equation to the form shown in your answer. Hint: use the Pythagorean theorem to determine the distances without using the absolute value symbol.

Good luck, and keep us posted.  4. Originally Posted by Leszek Luchowski is the Euclidean distance, in the complex plane, between and . Likewise, is the Euclidean distance between and .

Now the locus of points such that the sum of the distances between and two given points is equal to a given constant (greater than the distance between the two points) is an ellipse.

You do the math to transform the equation to the form shown in your answer. Hint: use the Pythagorean theorem to determine the distances without using the absolute value symbol.

Good luck, and keep us posted.
I'm sorry if I don't understand, but why would be the distance between z and -1?  5. It looks like these are typos. The distances are to -i and i respectively. The original equation means that the sum of the distances to these two points = 3. The geometrical definition of an ellipse is of this form.  6. Yes, I made a typo, or rather, a mistake due to careless writing. Sorry about that, and thanks for the correction.

Yes the distances are to and .  7. Ok, so let .
Our equation is        But then, if I'm not mistaken, it is wrong in the key, since x corresponds to a and y to b.  Bookmarks
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