Question

What is the modulus of a complex number?

Answer 1

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(cos theta + i sin theta)`), 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|=sqrt(a^2+b^2)`.