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?

Martín-Blas Pérez Pinilla · Accepted Answer · 2014-05-12T09:23:09.950

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.

edited May 12 '14 at 09:23

answered May 12 '14 at 06:18

Martín-Blas Pérez Pinilla

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Sadly enough ${\tt atan2(x,y)}\ne\arg(x,y)$. It's the other way around: ${\tt atan2(y,x)}=\arg(x,y)$. – Christian Blatter May 12 '14 at 08:40
True, I will edit. Thanks! – Martín-Blas Pérez Pinilla May 12 '14 at 09:21

score 0 · Answer 2 · answered May 12 '14 at 06:12

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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?

answered May 12 '14 at 06:12

Michael

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score 0 · Answer 3 · answered May 12 '14 at 09:39

$C_1$ 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.

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

3 Answers3