Complex Analysis Graphing Question

[kathrynag]

Homework Statement

I want to show $$z_{1}$$+($$z_{2}$$+$$z_{3}$$)=($$z_{1}$$+$$z_{2}$$)+$$z_{3}$$ with the use of a graph.

Homework Equations

The Attempt at a Solution

I am just cluless on how to graph. I know z=x+iy where the real part is on the x-axis and the imaginary part is on the y axis.

 

[Gib Z]

Well, each complex number can be represented by a vector in the Argand Plane. You should know how to add vectors, if not its easy to learn and is probably in your textbook. Basically it's just a matter of adding two of the vectors first, then the last, and showing that lands you in the same place as adding another pair, then the last. Ie Order doesn't matter.

 

[kathrynag]

ok, I think I understand. So, I have z1 and z2 and show what happens when I add z3 to it?

 

[NoMoreExams]

Each of them is a vector,

Did you draw z_1, then z_2 + z_3, now what happens when you add those 2 together?

Now what happens when you draw z_1 + z_2 and then add z_3 to it?