What is the modulus of a complex number?

1 Answer
May 11, 2015

In simple terms the modulus of a complex number is its size.

If you picture a complex number as a point on the complex plane, it is the distance of that point from the origin.

If a complex number is expressed in polar coordinates (i.e. as r(cosθ+isinθ)), then it's just the radius (r).

If a complex number is expressed in rectangular coordinates - i.e. in the form a+ib - then it's the length of the hypotenuse of a right angled triangle whose other sides are a and b.

From Pythagoras theorem we get: |a+ib|=a2+b2.