(4%2Bi).jpeg "(3+2i)(4+i)")
Multiplying Complex Numbers: (3 + 2i)(4 + i)
This article will explore the multiplication of two complex numbers: (3 + 2i) and (4 + i).
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 (i.e., i² = -1).
Multiplication Process
To multiply complex numbers, we can use the distributive property (also known as FOIL method) similar to multiplying binomials:
- First: Multiply the first terms of each complex number: (3)(4) = 12
- Outer: Multiply the outer terms: (3)(i) = 3i
- Inner: Multiply the inner terms: (2i)(4) = 8i
- Last: Multiply the last terms: (2i)(i) = 2i²
Now, we combine the results and simplify using the fact that i² = -1:
12 + 3i + 8i + 2i² = 12 + 3i + 8i + 2(-1) = 12 + 11i - 2
Final Result
Therefore, the product of (3 + 2i) and (4 + i) is:
(3 + 2i)(4 + i) = 10 + 11i