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If z = 2 + 2i, what is the value of z^2?

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

Options:

  1. 0
  2. 8i
  3. 8
  4. 4

Correct Answer: 8

Solution: 

z^2 = (2 + 2i)^2 = 4 + 8i - 4 = 8i.

If z = 2 + 2i, what is the value of z^2?

Practice Questions

Q1
If z = 2 + 2i, what is the value of z^2?
  1. 0
  2. 8i
  3. 8
  4. 4

Questions & Step-by-Step Solutions

If z = 2 + 2i, what is the value of z^2?
  • Step 1: Identify the value of z, which is 2 + 2i.
  • Step 2: Write the expression for z squared, which is (2 + 2i)^2.
  • Step 3: Use the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2.
  • Step 4: In our case, a = 2 and b = 2i. So, calculate a^2: 2^2 = 4.
  • Step 5: Calculate 2ab: 2 * 2 * 2i = 8i.
  • Step 6: Calculate b^2: (2i)^2 = 4i^2. Since i^2 = -1, this becomes 4 * -1 = -4.
  • Step 7: Combine all parts: 4 + 8i - 4.
  • Step 8: Simplify the expression: 4 - 4 + 8i = 0 + 8i.
  • Step 9: Therefore, z^2 = 8i.
  • Complex Numbers – Understanding the operations involving complex numbers, including squaring a complex number.
  • Algebraic Expansion – Applying the formula (a + b)^2 = a^2 + 2ab + b^2 to expand the expression.
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