# Argand diagrams

• Jul 31st 2006, 01:38 AM
kingkaisai2
Argand diagrams
Draw Argand diagrams to illustrate the (kz)*=kz*where k is a real number and z* means the conjugate of z

I know I am asking a lot so if you find it to troublesome to "draw" a diagram, can you please thoroughly describe what it looks like.
• Jul 31st 2006, 04:13 AM
topsquark
Quote:

Originally Posted by kingkaisai2
Draw Argand diagrams to illustrate the (kz)*=kz*where k is a real number and z* means the conjugate of z

I know I am asking a lot so if you find it to troublesome to "draw" a diagram, can you please thoroughly describe what it looks like.

On the Argand plane the complex number z = a + ib is simply the coordinate point (a, b). Thus z* = a - ib is the point (a, -b), or the point (a, b) reflected over the "x" (real) axis.

You can think of the complex numbers as vectors in the Argand plane. So by multiplying z by a real number k you are simply stretching the vector by a factor of k.

Now it's simply a matter of showing that the operations of stretching and reflecting the vector over the real axis are commutative, which should be obvious.

-Dan