# Complex numbers2

• March 21st, 2010, 12:02 PM
thyristor
Complex numbers2
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?
• March 21st, 2010, 12:41 PM
Leszek Luchowski
Re: Complex numbers2 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.
• March 21st, 2010, 01:53 PM
thyristor
Re: Complex numbers2
Quote:

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?
• March 21st, 2010, 03:42 PM
mathman
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.
• March 21st, 2010, 06:05 PM
Leszek Luchowski
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 .
• March 22nd, 2010, 12:10 PM
thyristor
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.