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).


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


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