(x+2i)(x-2i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (x + 2i)(x - 2i)

This article explores the multiplication of the complex numbers (x + 2i) and (x - 2i). We will use the distributive property and the fact that i² = -1 to simplify the expression.

The Distributive Property

We begin by applying the distributive property:

(x + 2i)(x - 2i) = x(x - 2i) + 2i(x - 2i)

Next, we distribute each term:

= x² - 2ix + 2ix - 4i²

Simplifying the Expression

Notice that the terms -2ix and +2ix cancel each other out. We are left with:

= x² - 4i²

Recall that i² = -1. Substituting this in, we get:

= x² - 4(-1)

= x² + 4

Conclusion

Therefore, the product of (x + 2i) and (x - 2i) is x² + 4. This demonstrates a key concept in complex numbers: multiplying a complex number by its conjugate results in a real number.