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If z = 1 + i, find z^2.

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Question: If z = 1 + i, find z^2.

Options:

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

Correct Answer: 1 + 2i

Solution: 

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

If z = 1 + i, find z^2.

Practice Questions

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

Questions & Step-by-Step Solutions

If z = 1 + i, find z^2.
Correct Answer: 2i
  • Step 1: Start with the given value of z, which is 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: a^2 = 1^2 = 1.
  • Step 5: Next, calculate 2ab: 2 * 1 * i = 2i.
  • Step 6: Now, calculate b^2: i^2. We know that i^2 = -1.
  • Step 7: Combine all the parts together: z^2 = 1 + 2i + (-1).
  • Step 8: Simplify the expression: 1 - 1 + 2i = 0 + 2i.
  • Step 9: Therefore, z^2 = 2i.
  • Complex Numbers – Understanding the operations involving complex numbers, including addition, multiplication, and the properties of the imaginary unit i.
  • Squaring a Binomial – Applying the formula (a + b)^2 = a^2 + 2ab + b^2 to compute the square of a complex number.
  • Imaginary Unit – Recognizing that i^2 = -1 and correctly applying this in calculations.
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