How Do You Find the Magnitude of a Complex Number?
The magnitude, or modulus, of a complex number in the form z = a + bi is the positive square root of the sum of the squares of a and b. In other words, |z| = sqrt(a^2 + b^2).
For example, in the complex number z = 3 + 4i, the magnitude is sqrt(3^2 + 4^2) = 5. Similarly, in the complex number z = 3 – 4i, the magnitude is sqrt(3^2 + (-4)^2) = 5.
Several corollaries come from the formula |z| = sqrt(a^2 + b^2). First, if the magnitude of a complex number is 0, then the complex number is equal to 0. It is also true that the magnitude of the product of two complex numbers is equal to the product of the magnitudes of both complex numbers. In other words, |z1 * z2| = |z1| * |z2|. This rule also applies to quotients; |z1 / z2| = |z1| / |z2|.