Find the square of each term. For example, the square of a real number (which is a single term) such as -5 is (-5) x (-5) = 25. The squared terms of a complex number (3 -- 2i) are (3) x (3) = 9 and (-2) x (-2) = 4. The squared terms of a vector R = (Rx; Ry; Rz) = (2; 3; 4) are (2 x 2) = 4, (3 x 3) = 9, and (4 x 4) = 16.
Add all the squared terms. For example, the sum of the squared terms of a complex number (3 -- 2i) is 9 + 4 = 13. The sum of the squared terms of a vector R = (2; 3; 4) is 4 + 9 + 16 = 29. The square of a real number appears as a single term so this step is omitted for real numbers.
Find the magnitude by calculating the square root of the sum of the squared terms. For example, for a real number such as -5, the magnitude is 5 = [(-5) x (-5)]^1/2 = [25]^1/2. The magnitude of the complex number (3 -- 2i) is 3.6 = [(3) x (3) + (-2) x (-2)]^1/2 = [9 + 4]^1/2 = [13]^1/2. The magnitude of the vector R = (2; 3; 4) = 5.4 = [(2 x 2) + (3 x 3) + (4 x 4)]^1/2 = [4 + 9 + 16]^1/2 = [29]^1/2.