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If z = 1 + i, what is the value of z^2? (2022)

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Question: If z = 1 + i, what is the value of z^2? (2022)

Options:

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

Correct Answer: 1 + 2i

Solution: 

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

If z = 1 + i, what is the value of z^2? (2022)

Practice Questions

Q1
If z = 1 + i, what is the value of z^2? (2022)
  1. 2i
  2. 1 + 2i
  3. 2
  4. 0

Questions & Step-by-Step Solutions

If z = 1 + i, what is the value of z^2? (2022)
  • Step 1: Identify the value of z, which is given as z = 1 + i.
  • Step 2: To find z^2, we need to calculate (1 + i)^2.
  • Step 3: Use the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2.
  • Step 4: Here, a = 1 and b = i. So, we calculate 1^2, 2(1)(i), and i^2.
  • Step 5: Calculate 1^2, which is 1.
  • Step 6: Calculate 2(1)(i), which is 2i.
  • Step 7: Calculate i^2. Remember that i^2 = -1.
  • Step 8: Now, combine all the results: 1 + 2i - 1.
  • Step 9: Simplify the expression: 1 - 1 + 2i = 2i.
  • Step 10: Therefore, the value of z^2 is 2i.
  • Complex Numbers – Understanding the properties and operations involving complex numbers, including addition, multiplication, and squaring.
  • Algebraic Expansion – Applying the binomial theorem or algebraic identities to expand expressions involving complex numbers.
  • Imaginary Unit – Recognizing that i^2 = -1 and correctly applying this in calculations.
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