What is the product of the complex numbers z1 = 1 + i and z2 = 1 - i?

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Question: What is the product of the complex numbers z1 = 1 + i and z2 = 1 - i?

Options:

Correct Answer: 2

Solution:

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

What is the product of the complex numbers z1 = 1 + i and z2 = 1 - i?

What is the product of the complex numbers z1 = 1 + i and z2 = 1 - i?

Step 1: Identify the complex numbers. We have z1 = 1 + i and z2 = 1 - i.
Step 2: Write down the multiplication of the two complex numbers: z1 * z2 = (1 + i)(1 - i).
Step 3: Use the distributive property (also known as the FOIL method) to multiply: (1 + i)(1 - i) = 1*1 + 1*(-i) + i*1 + i*(-i).
Step 4: Calculate each part: 1*1 = 1, 1*(-i) = -i, i*1 = i, and i*(-i) = -i^2.
Step 5: Combine the results: 1 - i + i - i^2.
Step 6: Notice that -i and +i cancel each other out: 1 - i + i = 1.
Step 7: Remember that i^2 = -1, so -(-1) = +1.
Step 8: Add the results together: 1 + 1 = 2.

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