Question

multiply and simplify the product.
(2i(4 - 5i))
select the product.

• (-2i)
• (2i)
• (-10 + 8i)
• (10 + 8i)

Explanation:

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

Step 1: Distribute the term

Distribute \( 2i \) to both terms inside the parentheses:

$$ 2i(4 - 5i) = (2i \cdot 4) - (2i \cdot 5i) $$

$$ = 8i - 10i^2 $$

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

Since the imaginary unit \( i \) is defined such that \( i^2 = -1 \), substitute \( -1 \) for \( i^2 \):

$$ 8i - 10(-1) $$

$$ = 8i + 10 $$

Step 3: Write in standard form

Rearrange the terms into standard complex number form, \( a + bi \):

$$ 10 + 8i $$

Answer:

\( 10 + 8i \) (the fourth option)