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What is the value of (1 + i)²?

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Question: What is the value of (1 + i)²?

Options:

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

Correct Answer: 2

Solution: 

(1 + i)² = 1² + 2(1)(i) + i² = 1 + 2i - 1 = 2i.

What is the value of (1 + i)²?

Practice Questions

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

Questions & Step-by-Step Solutions

What is the value of (1 + i)²?
  • Step 1: Start with the expression (1 + i)².
  • Step 2: Use the formula for squaring a binomial: (a + b)² = a² + 2ab + b².
  • Step 3: Identify a and b in our case: a = 1 and b = i.
  • Step 4: Calculate a²: 1² = 1.
  • Step 5: Calculate 2ab: 2(1)(i) = 2i.
  • Step 6: Calculate b²: i². Remember that i is the imaginary unit, and i² = -1.
  • Step 7: Combine all parts: 1 + 2i + (-1).
  • Step 8: Simplify: 1 - 1 + 2i = 0 + 2i.
  • Step 9: Final result: (1 + i)² = 2i.
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