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

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

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

Steps: 8

Step 1: Identify the complex numbers. Here, z1 = 1 + i and z2 = 1 - i.
Step 2: Write down the multiplication of z1 and z2: z1 * z2 = (1 + i)(1 - i).
Step 3: Use the formula for multiplying two binomials: (a + b)(c + d) = ac + ad + bc + bd. In our case, a = 1, b = i, c = 1, and d = -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, so we have 1 - i^2.
Step 7: Recall that i^2 = -1, so replace -i^2 with -(-1).
Step 8: Simplify the expression: 1 - (-1) = 1 + 1 = 2.