What does $\theta = \text{arg}(a,b)$ mean?

Question

I have this equation where an angle is calculated using following formula:

$$\theta = \text{arg}(C_1, C_2)$$

where $C_1, C_2$ are some numerical values. What exactly does it mean?

Answer 1

Likely, $$\arg(a,b)=\arg(a+bi),$$ where the second $\arg$ is the usual argument of a complex number.

In some programming languages there is a function $\tt atan2(y,x)$ with this meaning.

Answer 2

arg is usually a function operating on complex numbers. It gives the angle between the line joining the point to the origin and the positive real axis.

For example, arg$(i) = \pi/2+2k\pi $.

Where do you see this formula? More details?

Answer 3

$C_1$ is a point on the $x$-axis, $C_2$ is a point on the $y$-axis so $(C_1,C_2)$ is a point on the plane, as usual. Then $\arg(C_1,C_2)$ is (up to $2\pi$ additive multiples) simply the angle between the $x$-axis and the segment passing thru $(C_1,C_2)$ and the origin.