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

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Question: If z1 = 1 + i and z2 = 2 - 3i, find z1 * z2.

Options:

Correct Answer: 7 - i

Solution:

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

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

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

Correct Answer: 5 - i

Step 1: Identify the complex numbers. Here, z1 = 1 + i and z2 = 2 - 3i.
Step 2: Write down 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. Remember that i^2 = -1, so -3i^2 = 3.
Step 5: Combine all the results: 2 - 3i + 2i + 3.
Step 6: Combine like terms: (2 + 3) + (-3i + 2i) = 5 - i.
Step 7: Write the final result: z1 * z2 = 5 - i.

Complex Number Multiplication – The process of multiplying two complex numbers using the distributive property and combining like terms.