Simplify the expression. Show your step-by-step work.

Question

(2+3i)(8−5i)

Answer 1

To simplify the expression (2+3i)(8-5i), we can use the distributive property.

First, we will multiply the first terms of each expression:
2 * 8 = 16

Next, we will multiply the outer terms:
2 * (-5i) = -10i

Then, we will multiply the inner terms:
3i * 8 = 24i

Finally, we will multiply the last terms:
3i * (-5i) = -15i^2

To simplify the expression, we need to combine like terms. Since i^2 is equal to -1, we can substitute it into the expression:

16 - 10i + 24i - 15i^2

Simplifying further, we have:

16 - 10i + 24i - 15(-1)

16 - 10i + 24i + 15

Combining like terms, we get:

31 + 14i

So, the simplified expression is 31 + 14i.