Re: complex numbers and sets

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**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.

Re: complex numbers and sets

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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

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).

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