Use the FOIL method to find the terms of the following multiplication problem. $$ (6+6 i) \cdot(5-4 i) $$

Question

UpStudy AI · Accepted Answer

To solve (6 + 6i) · (5 – 4i) using the FOIL method, follow these steps:

1. First: Multiply the first terms in each binomial.  
  6 · 5 = 30

2. Outer: Multiply the outer terms.  
  6 · (–4i) = –24i

3. Inner: Multiply the inner terms.  
  6i · 5 = 30i

4. Last: Multiply the last terms in each binomial.  
  6i · (–4i) = –24i²

Now, combine the like terms:

- Combine the imaginary parts: –24i + 30i = 6i  
- Recall that i² = –1, so –24i² = –24(–1) = 24

Finally, add the real parts:
  30 (from the "First" term) + 24 (from the "Last" term) = 54

Thus, putting it all together, the product is:
  54 + 6i

So, the final result is 54 + 6i.
The product of (6 + 6i) and (5 - 4i) is 54 + 6i.

Use the FOIL method to find the terms of the following multiplication problem. \[ (6+6 i) \cdot(5-4 i) \]