(-6i)(3-2i)-(7i)(4i)

less than a minute read Jun 16, 2024

Simplifying Complex Expressions: (-6i)(3-2i)-(7i)(4i)

This article will guide you through simplifying the complex expression (-6i)(3-2i)-(7i)(4i). We will use the distributive property and the fact that i² = -1 to achieve our solution.

Step 1: Distribute

Let's begin by distributing the terms in the first part of the expression:

(-6i)(3-2i) = (-6i * 3) + (-6i * -2i) = -18i + 12i²

Now, let's distribute the terms in the second part of the expression:

-(7i)(4i) = -28i²

Step 2: Substitute i²

Remember that i² = -1. Substitute this value into our expression:

-18i + 12i² - 28i² = -18i + 12(-1) - 28(-1)

Step 3: Simplify

Now, let's simplify the expression:

-18i - 12 + 28 = -18i + 16

Conclusion

Therefore, the simplified form of the complex expression (-6i)(3-2i)-(7i)(4i) is -18i + 16.