# modulus

'Modulus' is a term with several meanings in mathematics. The modulus of a real
number is its positive value, shown by placing the number between vertical
lines: thus |–2| = |+2| = 2. The modulus (or absolute
value) of a complex number *z*,
where *z* = *x* + *iy*, is defined as √(*x*^{ 2} + *y *^{2}). If *z* is represented by a point in an Argand diagram, then its modulus *r*, is the distance from the origin to that point. Again, the term
modulus sometimes refers to a constant of proportionality. In logarithms,
if log* _{a}x* =

*k*log

*, where*

_{b}x*a*and

*b*are different bases,

*k*is known as the modulus.