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If z1 = 1 + i and z2 = 2 - i, find z1 * z2.

Practice Questions

Q1
If z1 = 1 + i and z2 = 2 - i, find z1 * z2.
  1. 3 + i
  2. 3 - i
  3. 2 + 3i
  4. 2 - 3i

Questions & Step-by-Step Solutions

If z1 = 1 + i and z2 = 2 - i, find z1 * z2.
Correct Answer: 3 + i
  • Step 1: Identify the complex numbers. Here, z1 = 1 + i and z2 = 2 - i.
  • Step 2: Write down the multiplication of the two complex numbers: z1 * z2 = (1 + i)(2 - i).
  • Step 3: Use the distributive property (also known as the FOIL method) to multiply the two complex numbers: (1 * 2) + (1 * -i) + (i * 2) + (i * -i).
  • Step 4: Calculate each part: 1 * 2 = 2, 1 * -i = -i, i * 2 = 2i, and i * -i = -i^2. Remember that i^2 = -1, so -i^2 = 1.
  • Step 5: Combine all the parts together: 2 - i + 2i + 1.
  • Step 6: Combine like terms: (2 + 1) + (-i + 2i) = 3 + i.
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