(-2-2)(-4-3i)(7+8i)

2 min read Jun 16, 2024

Multiplying Complex Numbers: A Step-by-Step Guide

This article will guide you through the process of multiplying the complex numbers (-2-2)(-4-3i)(7+8i). We'll break down each step to ensure a clear understanding of complex number multiplication.

Step 1: Multiply the First Two Complex Numbers

First, let's multiply (-2-2) and (-4-3i). We can use the distributive property (or FOIL method) to achieve this:

(-2-2)(-4-3i) = (-2)(-4) + (-2)(-3i) + (-2)(-4) + (-2)(-3i)
                 = 8 + 6i + 8 + 6i
                 = 16 + 12i

Step 2: Multiply the Result by the Third Complex Number

Now we have (16 + 12i) to multiply by (7+8i). Again, we'll use the distributive property:

(16 + 12i)(7+8i) = (16)(7) + (16)(8i) + (12i)(7) + (12i)(8i)
                 = 112 + 128i + 84i + 96i^2

Step 3: Simplify Using i^2 = -1

Remember that i^2 is defined as -1. Substituting this into our expression, we get:

112 + 128i + 84i + 96i^2 = 112 + 128i + 84i + 96(-1)
                           = 112 + 128i + 84i - 96
                           = 16 + 212i

Final Result

Therefore, the product of (-2-2)(-4-3i)(7+8i) is 16 + 212i.