absolute value

In mathematics, the value, or magnitude, of a number irrespective of its sign. The absolute value of a number n is written |n| (or sometimes as mod n), and is defined as the positive square root of n². For example, the numbers −5 and 5 have the same absolute value:

|5| = |−5| = 5

For a complex number, the absolute value is its distance to the origin when it is plotted on an Argand diagram, and can be calculated (without plotting) by applying Pythagoras' theorem. By definition, the absolute value of any complex number a + ib (where a and b are real numbers and i is the square root of −1) is given by the expression:

|a + ib| = √(a² + b²)