Question

use distributive property to show 4i [(3i) + (-5i-6)] simplest form

Answer 1

Start by simplifying inside the brackets:
(3i) + (-5i - 6) = 3i - 5i - 6 = -2i - 6.

Now distribute 4i:
4i(-2i - 6) = 4i(-2i) + 4i(-6) = -8i^2 - 24i.

Use i^2 = -1:
-8i^2 - 24i = -8(-1) - 24i = 8 - 24i.

Answer: 8 - 24i (which can also be written as 8(1 - 3i)).