(4-5i)(12+11i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (4 - 5i)(12 + 11i)

This article will guide you through the process of multiplying the complex numbers (4 - 5i) and (12 + 11i).

Understanding Complex Numbers

Before we start, let's briefly review the concept of complex numbers.

A complex number is a number 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).

Multiplying Complex Numbers

To multiply complex numbers, we use the distributive property, similar to how we multiply binomials.

1. Expand the product:

   (4 - 5i)(12 + 11i) = (4 * 12) + (4 * 11i) + (-5i * 12) + (-5i * 11i)

2. Simplify:

   48 + 44i - 60i - 55i²

3. Substitute i² with -1:

   48 + 44i - 60i + 55

4. Combine real and imaginary terms:

   (48 + 55) + (44 - 60)i

5. Final Result:

   103 - 16i

Therefore, the product of (4 - 5i) and (12 + 11i) is 103 - 16i.

Key Points

• The distributive property is crucial for multiplying complex numbers.
• Remember that i² = -1.
• Combine real and imaginary terms to express the final answer in the standard form a + bi.