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If z = 2 + 2i, what is the value of z^2?
Practice Questions
Q1
If z = 2 + 2i, what is the value of z^2?
0
8i
8
4
Questions & Step-by-Step Solutions
If z = 2 + 2i, what is the value of z^2?
Steps
Concepts
Step 1: Identify the value of z, which is 2 + 2i.
Step 2: Write the expression for z squared, which is (2 + 2i)^2.
Step 3: Use the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2.
Step 4: In our case, a = 2 and b = 2i. So, calculate a^2: 2^2 = 4.
Step 5: Calculate 2ab: 2 * 2 * 2i = 8i.
Step 6: Calculate b^2: (2i)^2 = 4i^2. Since i^2 = -1, this becomes 4 * -1 = -4.
Step 7: Combine all parts: 4 + 8i - 4.
Step 8: Simplify the expression: 4 - 4 + 8i = 0 + 8i.
Step 9: Therefore, z^2 = 8i.
No concepts available.
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