Abs

The absolute value of a number, or the magnitude of a complex number.

For a non-negative real number, Abs(x) returns x.

For a negative real number, Abs(x) returns -x.

For a complex number, a + bj, Abs(x) returns the magnitude, equal to [math]\displaystyle{ \sqrt{a^2+b^2} }[/math].

Complex numbers

A complex number can be written in standard (cartesian) form as [math]\displaystyle{ a + b j }[/math], or in polar form as [math]\displaystyle{ r e^{\theta j} }[/math]. Given a complex number, x, Abs(x) gives r, the magnitude from the polar form. The [math]\displaystyle{ \theta }[/math] is given by either ComplexRadians (or ComplexDegrees).

Examples

Abs(0) → 0

Abs(-0.123) → 0.123

Abs(4.534) → 4.534

Abs(-INF) → INF

Abs(-4-3j) → 5

Abs(1j) → 1

See Also

• Sign(x)
• Complex Numbers
• ComplexRadians, ComplexDegrees, ImPart, RealPart