# Argand Diagram

• Jan 7th 2008, 01:52 AM
SengNee
Argand Diagram
$\displaystyle z = x + yi$

What is the uses of modulus of , $\displaystyle r$ and arg , θ in an Argand diagram?
• Jan 7th 2008, 03:42 AM
$\displaystyle (r, \theta)$ are the polar coordinates of z
• Jan 7th 2008, 09:23 PM
SengNee
What is polar coordinate?
• Jan 7th 2008, 09:42 PM
Jhevon
Quote:

Originally Posted by SengNee
What is polar coordinate?

we know that the number z = x + iy can be graphed as a dot in the Argand plane at the point (x,y) correct? r is the legth of the line connecting the origin to (x,y) and $\displaystyle \theta$ is the angle this line makes with the positive real-axis
• Jan 8th 2008, 12:52 AM
SengNee
I know that:
r=|z|=length of z
$\displaystyle \theta$=the angle this line makes with the positive real-axis

I ask about what their uses, how we apply them to solve our daily problems?
• Jan 8th 2008, 01:29 AM
These have thousands of applications. One of the simplest is that if |z| = r and $\displaystyle \arg (z) = \theta$ then $\displaystyle |z^n| = r^n$ and $\displaystyle \arg (z^n) = n \theta$.