Final answer:
When real numbers a and b are the components of a complex number a + bi, the product of the complex number and its conjugate a - bi is the real number a^2 + b^2.
Step-by-step explanation:
If a and b are real numbers, then the product of a + bi and a -bi is a real number given by the sum of the squares of a and b. The product yields a2 + b2, as the complex parts cancel out. For example, if a = 3 and b = 4i, then the product a * a is (3 + 4i)(3 - 4i) which simplifies to 9 + 16, thus the product is 25. This demonstrates one of the fundamental properties of complex numbers, specifically when multiplying a complex number by its complex conjugate.