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

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

Options:

  1. 2
  2. 0
  3. 1
  4. 1 + 0i

Correct Answer: 2

Solution: 

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

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

Practice Questions

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

Questions & Step-by-Step Solutions

What is the product of (1 + i) and (1 - i)?
  • Step 1: Identify the two complex numbers we are multiplying: (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.
  • Step 4: Multiply the first terms: 1 * 1 = 1.
  • Step 5: Multiply the outer terms: 1 * -i = -i.
  • Step 6: Multiply the inner terms: i * 1 = i.
  • Step 7: Multiply the last terms: i * -i = -i^2.
  • Step 8: Combine all the results: 1 - i + i - i^2.
  • Step 9: Notice that -i and +i cancel each other out: 1 - i + i = 1.
  • Step 10: Now we have: 1 - i^2.
  • Step 11: Recall that i^2 = -1, so replace -i^2 with -(-1).
  • Step 12: This simplifies to: 1 + 1 = 2.
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