Question

Multiply and simplify the product. –12i × 3i select the product. 36 -36 36i -36i multiply and simplify the product. 2i(4 – 5i) select the product. –2i 2i –10 8i 10 8i

Answer 1

The product of −12i and 3i is −36. The product of 2i and (4 – 5i) simplifies to 8i + 10.

Step-by-step explanation:

To multiply and simplify the product −12i × 3i, we need to remember that the product of two complex numbers involves the product of their real parts and their imaginary parts. The number i represents the square root of −1, so i² is actually −1. Therefore, the multiplication gives us −12 × 3 × i², which simplifies to −(12· 3) × (−1), resulting in −36.

Next, we must multiply and simplify 2i(4 – 5i). We distribute the 2i across the terms inside the parentheses: 2i × 4 – 2i × 5i. This gives us 8i – 10i². Since i² is −1, the expression simplifies to 8i – 10(−1), which gives us 8i + 10.