If z = 2 + 2i, find z².

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Question: If z = 2 + 2i, find z².

Options:

Correct Answer: 8

Solution:

z² = (2 + 2i)² = 4 + 8i - 4 = 8i.

If z = 2 + 2i, find z².

If z = 2 + 2i, find z².

Step 1: Start with the given value of z, which is 2 + 2i.
Step 2: To find z², we need to calculate (2 + 2i)².
Step 3: Use the formula for squaring a binomial: (a + b)² = a² + 2ab + b².
Step 4: Here, a = 2 and b = 2i. So, calculate a²: 2² = 4.
Step 5: Next, calculate 2ab: 2 * 2 * 2i = 8i.
Step 6: Now, calculate b²: (2i)² = 4i². Since i² = -1, this becomes 4 * -1 = -4.
Step 7: Combine all the parts: 4 + 8i - 4.
Step 8: Simplify the expression: 4 - 4 + 8i = 0 + 8i.
Step 9: Therefore, z² = 8i.

Complex Numbers – Understanding the operations involving complex numbers, including squaring a complex number.
Algebraic Expansion – Applying the formula (a + b)² = a² + 2ab + b² correctly.