Question

Determine the simplest form of (6-8i)(6+8i)

Answer 1

The simplest form of the product (6-8i)(6+8i) is obtained by using the foil method, which gives us 100 after simplifying and combining like terms.

Step-by-step explanation:

To determine the simplest form of (6-8i)(6+8i), we can use the foil method to multiply the two complex numbers.

First, multiply the first terms: 6 × 6 = 36.

Next, multiply the outer terms: 6 × 8i = 48i.

Then, multiply the inner terms: -8i × 6 = -48i.

Lastly, multiply the last terms: -8i × 8i = -64i². We know that i² = -1, so -64i² = -64 × -1.

This results in 64. Adding all these up, we get 36 + 48i - 48i + 64. The imaginary parts cancel each other out, so we are left with 36 + 64.

Summing the real parts gives us 36 + 64 = 100. Therefore, the product in its simplest form is 100.