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

Practice Questions

Q1
What is the product of the complex numbers (1 + i) and (1 - i)? (2023) 2023
  1. 2
  2. 0
  3. 1
  4. 1 + 0i

Questions & Step-by-Step Solutions

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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