Thread: 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.

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 and see what "form" these relations then take.

Originally Posted by Prove It

Try writing 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

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).

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