Question

Simplify the expression (5 - 2i) (3 + 4i) - (-6 + 2i) as much as possible.

Answer 1

To simplify the expression (5 - 2i) (3 + 4i) - (-6 + 2i), multiply the terms within the parentheses, simplify any terms with a variable raised to a power, and combine like terms.

Step-by-step explanation:

To simplify the expression (5 - 2i) (3 + 4i) - (-6 + 2i), we can use the distributive property. First, multiply the terms within the first parentheses with the terms within the second parentheses:

1. (5)(3) + (5)(4i) + (-2i)(3) + (-2i)(4i)
2. 15 + 20i - 6i - 8i²

Next, simplify the term with a variable raised to a power:

1. 15 + 20i - 6i - 8(-1)
2. 15 + 20i - 6i + 8

Finally, combine like terms:

1. 23 + 14i.