(4-3i).jpeg "(6+2i)(4-3i)")
Multiplying Complex Numbers: (6 + 2i)(4 - 3i)
This article will guide you through multiplying complex numbers, specifically the product of (6 + 2i) and (4 - 3i).
Understanding Complex Numbers
Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit, defined as the square root of -1 (i² = -1).
The Multiplication Process
Multiplying complex numbers is similar to multiplying binomials. We use the distributive property (also known as FOIL method) to expand the expression:
(6 + 2i)(4 - 3i) = 6(4 - 3i) + 2i(4 - 3i)
Now, we distribute:
= 24 - 18i + 8i - 6i²
Remember that i² = -1. Substituting this:
= 24 - 18i + 8i + 6
Finally, combine the real and imaginary terms:
= (24 + 6) + (-18 + 8)i
= 30 - 10i
The Result
Therefore, the product of (6 + 2i) and (4 - 3i) is 30 - 10i.
Summary
Multiplying complex numbers involves applying the distributive property, substituting i² with -1, and combining like terms to arrive at a simplified complex number in the form a + bi.