Apply the Distributive Property to show 3i [(2i) + (-3i - 5)] in its simplest form.
To apply the distributive property and simplify the expression 3i [(2i) + (-3i - 5)], we will distribute 3i to both terms within the parentheses.
3i (2i) + 3i (-3i) + 3i(-5)
Now, we will simplify each term:
1. Multiplying 3i (2i):
3i (2i) = 6i² = 6(-1) = -6
2. Multiplying 3i (-3i):
3i (-3i) = -9i² = -9(-1) = 9
3. Multiplying 3i (-5):
3i (-5) = -15i
Now, combining the simplified terms, we get:
-6 + 9 + (-15i) = 3 - 15i
Therefore, 3i [(2i) + (-3i - 5)] simplifies to 3 - 15i.