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If z = 2 + 2i, find z².

Practice Questions

Q1
If z = 2 + 2i, find z².
  1. 0
  2. 8i
  3. 8
  4. 4 + 8i

Questions & Step-by-Step Solutions

If z = 2 + 2i, find z².
  • Step 1: Start with the given value of z, which is 2 + 2i.
  • Step 2: To find z², we need to calculate (2 + 2i)².
  • Step 3: Use the formula for squaring a binomial: (a + b)² = a² + 2ab + b².
  • Step 4: Here, a = 2 and b = 2i. So, calculate a²: 2² = 4.
  • Step 5: Next, calculate 2ab: 2 * 2 * 2i = 8i.
  • Step 6: Now, calculate b²: (2i)² = 4i². Since i² = -1, this becomes 4 * -1 = -4.
  • Step 7: Combine all the parts: 4 + 8i - 4.
  • Step 8: Simplify the expression: 4 - 4 + 8i = 0 + 8i.
  • Step 9: Therefore, z² = 8i.
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