(1-3i).jpeg "(1+3i)(1-3i)")
Multiplying Complex Numbers: (1 + 3i)(1 - 3i)
This article will demonstrate how to multiply the complex numbers (1 + 3i) and (1 - 3i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.
Multiplying Complex Numbers
To multiply complex numbers, we use the distributive property (also known as FOIL - First, Outer, Inner, Last) just like we do with binomials.
Step 1: Apply the distributive property. (1 + 3i)(1 - 3i) = 1(1) + 1(-3i) + 3i(1) + 3i(-3i)
Step 2: Simplify the terms. = 1 - 3i + 3i - 9i²
Step 3: Remember that i² = -1. Substitute this value. = 1 - 3i + 3i - 9(-1)
Step 4: Combine the real and imaginary terms. = 1 + 9 = 10
Therefore, (1 + 3i)(1 - 3i) = 10
Conclusion
As you can see, multiplying complex numbers is a straightforward process that involves using the distributive property and simplifying the resulting terms. The result of (1 + 3i)(1 - 3i) is a real number, which is 10.