The Art of Mathematics

Help 6.15

arg — argument of the complex number

1. Definition

z = a + i b, where a and b are real numbers

its argument is defined as

arg(z) ≡ arctan(b /a), for a > 0;
arg(z) ≡ π /2, for a = 0 and b > 0;
arg(z) ≡ −π /2, for a = 0 and b < 0;
arg(z) ≡ arctan(b /a) + π, for a < 0 and b ≥ 0;
arg(z) ≡ arctan(b /a) − π, for a < 0 and b < 0;
arg(z) ≡ 0, for z = 0.

In words it is the angle in complex plane between positive direction of the real axis and radius-vector of the number.

From the definition it follows that function codomain is (−π, π].

2. How to use

To calculate argument of the number:

arg(2+i);

To get argument of the current result:

arg(rslt);

To get argument of the number z in calculator memory:

arg(mem[z]);

3. Support

Argument of the complex number is supported in professional version of the Librow calculator.