Modulus

The modulus of a vector r, usually written |r|, or sometimes simply r, is defined to be the length of the vector r. If r is written in terms of three orthonormal vectors (ie: mutually perpendicular vectors of unit length), i, j and k such that:

r=xi+yj+zk,

the modulus of r is the non-negative square root of x²+y²+z².

It should be noted that the modulus of a vector is a scalar?.

Moduli are also used in complex numbers: if Z=a+bi where i is defined to be the square root of -1, the modulus of Z is defined to be the non-negative square root of a²+b². This is used in the generation of some fractals - the bailout value for the Mandelbrot Set is often set to be when the modulus of the current value of Z is greater than 2.