Simplify:
left-parenthesis 2 plus 3 i right-parenthesis left-parenthesis 4 minus i right-parenthesis
To simplify the expression, we will multiply the terms inside the parentheses:
(2 + 3i)(4 - i)
Using the distributive property, we can expand the expression:
= 2(4) + 2(-i) + 3i(4) + 3i(-i)
Simplifying each term:
= 8 - 2i + 12i - 3i^2
Since i^2 is equal to -1, we can substitute:
= 8 - 2i + 12i - 3(-1)
= 8 - 2i + 12i + 3
Combining like terms:
= (8 + 3) + (-2i + 12i)
= 11 + 10i
So, the simplified expression is 11 + 10i.