# Thread: complex numbers and sets

1. ## complex numbers and sets

When given the sets X = { z is complex, mod(z) < 2}, Y = { z is complex, z - z* = 2i} where z* is the complex conjugate, draw these on an argand diagram.

2. ## Re: complex numbers and sets

Originally Posted by qwerty31
When given the sets X = { z is complex, mod(z) < 2}, Y = { z is complex, z - z* = 2i} where z* is the complex conjugate, draw these on an argand diagram.
Try writing \displaystyle \displaystyle \begin{align*} z = x + i\,y \end{align*} and see what "form" these relations then take.

3. ## Re: complex numbers and sets

Originally Posted by Prove It
Try writing \displaystyle \displaystyle \begin{align*} z = x + i\,y \end{align*} and see what "form" these relations then take.
I got that the first one is a circle with radius 2 and under...for the second one I seem to get y = 1, and Im not too sure about that

4. ## Re: complex numbers and sets

Originally Posted by qwerty31
I got that the first one is a circle with radius 2 and under...for the second one I seem to get y = 1, and Im not too sure about that
No, the first is not the circle with radius 2 and under, it's the circle with radius LESS than 2.

The second is correct. So it's a horizontal line where y = 1 (or where Im(z) = 1).

5. ## Re: complex numbers and sets

Originally Posted by Prove It
No, the first is not the circle with radius 2 and under, it's the circle with radius LESS than 2.

The second is correct. So it's a horizontal line where y = 1 (or where Im(z) = 1).
Oh, I forgot to put the 'less than or equal to' sign for the first one, sorry about that! And thank you