Question

multiply and simplify the product.
\\(-12i \times 3i\\)
select the product.
36
-36
36i
-36i

Explanation:

🆕 New Concept Discovered: Operations with Complex Numbers
Working with the imaginary unit where \( i^2 = -1 \)

Step 1: Multiply the coefficients and the imaginary units

Group the real coefficients together and the imaginary units together:

$$ (-12 \times 3) \times (i \times i) $$

Multiply the real numbers:

$$ -12 \times 3 = -36 $$

Multiply the imaginary units:

$$ i \times i = i^2 $$

Combine them:

$$ -36i^2 $$

Step 2: Simplify using the definition of \( i \)

The imaginary unit \( i \) is defined such that its square is equal to \( -1 \):

$$ i^2 = -1 $$

Substitute \( -1 \) for \( i^2 \) in the expression:

$$ -36(-1) $$

Multiply the values:

$$ 36 $$

Answer:

36