What is the modulus of the complex number 𝑎 plus 𝑏𝑖, where 𝑎 and 𝑏 are real?
If we consider the general complex number 𝑧 equals 𝑥 plus 𝑖𝑦 where 𝑥 and 𝑦 are real and 𝑖 is equal to the square root of negative one, then the square root of 𝑥 squared plus 𝑦 squared is the modulus or absolute value of 𝑧. This is denoted as shown. We find the sum of the squares of the real and imaginary parts of the number and then square root the answer. The real part of our complex number is equal to 𝑎, and the imaginary part is equal to 𝑏. This means that the modulus of the complex number 𝑎 plus 𝑏𝑖 is the square root of 𝑎 squared plus 𝑏 squared.