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If z = 1 + i, find z^2.
If z = 1 + i, find z^2.
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Practice Questions
1 question
Q1
If z = 1 + i, find z^2.
2i
2
1 + 2i
0
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z^2 = (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i.
Questions & Step-by-step Solutions
1 item
Q
Q: If z = 1 + i, find z^2.
Solution:
z^2 = (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i.
Steps: 9
Show Steps
Step 1: Start with the given value of z, which is 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.
Step 4: Here, a = 1 and b = i. So, we calculate: a^2 = 1^2 = 1.
Step 5: Next, calculate 2ab: 2 * 1 * i = 2i.
Step 6: Now, calculate b^2: i^2. We know that i^2 = -1.
Step 7: Combine all the parts together: z^2 = 1 + 2i + (-1).
Step 8: Simplify the expression: 1 - 1 + 2i = 0 + 2i.
Step 9: Therefore, z^2 = 2i.
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