What is the product of (1 + i) and (1 - i)?

What is the product of (1 + i) and (1 - i)?

Step 1: Identify the two complex numbers we are multiplying: (1 + i) and (1 - i).
Step 2: Use the formula for multiplying two binomials: (a + b)(c + d) = ac + ad + bc + bd.
Step 3: In our case, a = 1, b = i, c = 1, and d = -i.
Step 4: Multiply the first terms: 1 * 1 = 1.
Step 5: Multiply the outer terms: 1 * -i = -i.
Step 6: Multiply the inner terms: i * 1 = i.
Step 7: Multiply the last terms: i * -i = -i^2.
Step 8: Combine all the results: 1 - i + i - i^2.
Step 9: Notice that -i and +i cancel each other out: 1 - i + i = 1.
Step 10: Now we have: 1 - i^2.
Step 11: Recall that i^2 = -1, so replace -i^2 with -(-1).
Step 12: This simplifies to: 1 + 1 = 2.

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