Distribute to simplify the expression (3i + 4)(−2i − 5)
.(1 point)
+ i
To simplify the expression (3i + 4)(-2i - 5), we can use the distributive property.
First, distribute the 3i to both terms inside the second parentheses:
(3i)(-2i) + (3i)(-5)
Next, distribute the 4 to both terms inside the second parentheses:
(4)(-2i) + (4)(-5)
Simplify each term:
(3i)(-2i) = -6i^2
Since i^2 is equal to -1, we can substitute -1 for i^2:
-6(-1) = 6
(3i)(-5) = -15i
(4)(-2i) = -8i
(4)(-5) = -20
Now, combine like terms:
6 + (-15i) + (-8i) + (-20)
Combine the constants:
6 + (-20) = -14
Combine the i terms:
(-15i) + (-8i) = -23i
The simplified expression is: -14 - 23i