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If z = 1 + i, what is the value of z²? (2022)

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Question: If z = 1 + i, what is the value of z²? (2022)

Options:

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

Correct Answer: 1 + 2i

Exam Year: 2022

Solution: 

z² = (1 + i)² = 1² + 2(1)(i) + i² = 1 + 2i - 1 = 2i.

If z = 1 + i, what is the value of z²? (2022)

Practice Questions

Q1
If z = 1 + i, what is the value of z²? (2022)
  1. 0
  2. 2i
  3. 2
  4. 1 + 2i

Questions & Step-by-Step Solutions

If z = 1 + i, what is the value of z²? (2022)
  • Step 1: Start with the value of z, which is 1 + i.
  • Step 2: To find z², we need to calculate (1 + i)².
  • Step 3: Use the formula for squaring a binomial: (a + b)² = a² + 2ab + b².
  • Step 4: Here, a = 1 and b = i. So, we calculate 1², 2(1)(i), and i².
  • Step 5: Calculate 1², which is 1.
  • Step 6: Calculate 2(1)(i), which is 2i.
  • Step 7: Calculate i². Remember that i² = -1.
  • Step 8: Now combine all the parts: 1 + 2i - 1.
  • Step 9: The 1 and -1 cancel each other out, leaving us with 2i.
  • Step 10: Therefore, the value of z² is 2i.
  • Complex Numbers – Understanding the operations involving complex numbers, including addition, multiplication, and the properties of imaginary units.
  • Algebraic Expansion – Applying the binomial theorem or algebraic identities to expand expressions involving complex numbers.
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