# complex numbers and sets

• May 2nd 2012, 06:48 AM
qwerty31
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.
• May 2nd 2012, 07:02 AM
Prove It
Re: complex numbers and sets
Quote:

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 \begin{align*} z = x + i\,y \end{align*} and see what "form" these relations then take.
• May 2nd 2012, 07:05 AM
qwerty31
Re: complex numbers and sets
Quote:

Originally Posted by Prove It
Try writing \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
• May 2nd 2012, 07:09 AM
Prove It
Re: complex numbers and sets
Quote:

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).
• May 2nd 2012, 07:10 AM
qwerty31
Re: complex numbers and sets
Quote:

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 :D