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If z1 = 1 + i and z2 = 2 - 3i, what is z1 * z2?

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Question: If z1 = 1 + i and z2 = 2 - 3i, what is z1 * z2?

Options:

  1. 5 - i
  2. 8 - i
  3. 7 + i
  4. 1 + 5i

Correct Answer: 5 - i

Solution: 

z1 * z2 = (1 + i)(2 - 3i) = 2 - 3i + 2i - 3i^2 = 2 - i + 3 = 5 - i.

If z1 = 1 + i and z2 = 2 - 3i, what is z1 * z2?

Practice Questions

Q1
If z1 = 1 + i and z2 = 2 - 3i, what is z1 * z2?
  1. 5 - i
  2. 8 - i
  3. 7 + i
  4. 1 + 5i

Questions & Step-by-Step Solutions

If z1 = 1 + i and z2 = 2 - 3i, what is z1 * z2?
  • Step 1: Identify the complex numbers. Here, z1 = 1 + i and z2 = 2 - 3i.
  • Step 2: Write the multiplication of the two complex numbers: z1 * z2 = (1 + i)(2 - 3i).
  • Step 3: Use the distributive property (also known as the FOIL method for binomials) to multiply: (1 * 2) + (1 * -3i) + (i * 2) + (i * -3i).
  • Step 4: Calculate each part: 1 * 2 = 2, 1 * -3i = -3i, i * 2 = 2i, and i * -3i = -3i^2.
  • Step 5: Remember that i^2 = -1, so -3i^2 becomes -3 * -1 = 3.
  • Step 6: Combine all the parts together: 2 - 3i + 2i + 3.
  • Step 7: Combine like terms: (2 + 3) + (-3i + 2i) = 5 - i.
  • Step 8: The final result is z1 * z2 = 5 - i.
  • Complex Number Multiplication – The process of multiplying two complex numbers using the distributive property and the fact that i^2 = -1.
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