Find the value of z^2 if z = 1 + i.

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Q: Find the value of z^2 if z = 1 + i.

Solution: z^2 = (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i.

Steps: 9

Step 1: Identify the value of z. Here, z = 1 + i.
Step 2: To find z^2, we need to calculate (1 + i)^2.
Step 3: Use the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2. In our case, a = 1 and b = i.
Step 4: Calculate a^2: 1^2 = 1.
Step 5: Calculate 2ab: 2 * 1 * i = 2i.
Step 6: Calculate b^2: i^2. We know that i^2 = -1.
Step 7: Now combine all the parts: 1 + 2i + (-1).
Step 8: Simplify the expression: 1 - 1 + 2i = 0 + 2i.
Step 9: Therefore, z^2 = 2i.