# Math Help - Argand Diagram

1. ## Argand Diagram

$z = x + yi$

What is the uses of modulus of , $r$ and arg , θ in an Argand diagram?

2. $(r, \theta)$ are the polar coordinates of z

3. What is polar coordinate?

4. 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 $\theta$ is the angle this line makes with the positive real-axis

5. I know that:
r=|z|=length of z
$\theta$=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?

6. how we apply them to solve our daily problems?
These have thousands of applications. One of the simplest is that if |z| = r and $\arg (z) = \theta$ then $|z^n| = r^n$ and $\arg (z^n) = n \theta$.

7. Originally Posted by SengNee
I ask about what their uses, how we apply them to solve our daily problems?
The shortest route between two truths in the real domain passes through the complex domain. -Hadamard