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(4-5i)(-1-7i)

2 min read Jun 16, 2024
(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:

  1. Multiply the first terms: (4)(-1) = -4
  2. Multiply the outer terms: (4)(-7i) = -28i
  3. Multiply the inner terms: (-5i)(-1) = 5i
  4. 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.

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