Apply the Distributive Property to show 3i[(2i) + (-3i - 5)] in its simplest form.
Using the distributive property, we can distribute the 3i to both terms inside the parentheses:
3i * (2i) + 3i * (-3i - 5)
Simplifying each term inside the parentheses:
3i * (2i) + 3i * (-3i) + 3i * (-5)
Simplifying each product:
6i^2 - 9i^2 - 15i
Since i^2 = -1, we can substitute the values:
6(-1) - 9(-1) - 15i
Simplifying the multiplication:
-6 + 9 - 15i
Combining like terms:
3 - 15i
Therefore, 3i[(2i) + (-3i - 5)] simplifies to 3 - 15i.