What is the product of the complex numbers 2 + 3i and 4 - i? (2021)

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Question: What is the product of the complex numbers 2 + 3i and 4 - i? (2021)

Options:

Correct Answer: 11 + 10i

Solution:

(2 + 3i)(4 - i) = 8 - 2i + 12i - 3i^2 = 8 + 10i + 3 = 11 + 10i.

What is the product of the complex numbers 2 + 3i and 4 - i? (2021)

What is the product of the complex numbers 2 + 3i and 4 - i? (2021)

Step 1: Identify the complex numbers to multiply: 2 + 3i and 4 - i.
Step 2: Use the distributive property (also known as the FOIL method) to multiply the two complex numbers.
Step 3: Multiply the first terms: 2 * 4 = 8.
Step 4: Multiply the outer terms: 2 * -i = -2i.
Step 5: Multiply the inner terms: 3i * 4 = 12i.
Step 6: Multiply the last terms: 3i * -i = -3i^2. (Remember that i^2 = -1, so -3i^2 = 3.)
Step 7: Combine all the results: 8 - 2i + 12i + 3.
Step 8: Combine like terms: 8 + 3 = 11 and -2i + 12i = 10i.
Step 9: Write the final result: 11 + 10i.

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