(-1-7i).jpeg "(4-5i)(-1-7i)")
Multiplying Complex Numbers: (4-5i)(-1-7i)
This article will guide you through multiplying the complex numbers (4-5i) and (-1-7i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where:
- a and b are real numbers
- i is the imaginary unit, defined as the square root of -1 (i.e., i² = -1)
Multiplying Complex Numbers
To multiply complex numbers, we use the distributive property (often referred to as FOIL). Here's how it works:
- Multiply the first terms: (4)(-1) = -4
- Multiply the outer terms: (4)(-7i) = -28i
- Multiply the inner terms: (-5i)(-1) = 5i
- Multiply the last terms: (-5i)(-7i) = 35i²
Now, remember that i² = -1. So, we can simplify the last term: 35i² = 35(-1) = -35.
Combining Terms
Now, let's combine all the terms:
-4 -28i + 5i - 35
Combining the real and imaginary terms, we get:
(-4 - 35) + (-28 + 5)i
Final Answer
Therefore, the product of (4-5i) and (-1-7i) is -39 - 23i.