What is the product of the complex numbers (1 + i) and (1 - i)? (2023) 2023

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Question: What is the product of the complex numbers (1 + i) and (1 - i)? (2023) 2023

Options:

Correct Answer: 2

Exam Year: 2023

Solution:

(1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 2.

What is the product of the complex numbers (1 + i) and (1 - i)? (2023) 2023

What is the product of the complex numbers (1 + i) and (1 - i)? (2023) 2023

Step 1: Identify the complex numbers. We have (1 + i) and (1 - i).
Step 2: Use the formula for multiplying two binomials: (a + b)(c - d) = ac + ad - bc - bd.
Step 3: In our case, a = 1, b = i, c = 1, and d = i. So we calculate: (1)(1) + (1)(-i) + (i)(1) + (i)(-i).
Step 4: Calculate each part: (1)(1) = 1, (1)(-i) = -i, (i)(1) = i, and (i)(-i) = -i^2.
Step 5: Remember that i^2 = -1. So, -i^2 = -(-1) = 1.
Step 6: Now combine all parts: 1 - i + i + 1.
Step 7: The -i and +i cancel each other out, leaving us with 1 + 1 = 2.

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