Find the value of (1 + i)^2.

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Question: Find the value of (1 + i)^2.

Options:

Correct Answer: 2

Solution:

(1 + i)^2 = 1^2 + 2(1)(i) + i^2 = 1 + 2i - 1 = 2i.

Find the value of (1 + i)^2.

Find the value of (1 + i)^2.

Correct Answer: 2i

Step 1: Start with the expression (1 + i)^2.
Step 2: Use the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2.
Step 3: Here, a = 1 and b = i. So, we substitute: (1 + i)^2 = 1^2 + 2(1)(i) + i^2.
Step 4: Calculate 1^2, which is 1.
Step 5: Calculate 2(1)(i), which is 2i.
Step 6: Calculate i^2. Remember that i is the imaginary unit, and 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: The final result is 2i.

Complex Numbers – Understanding the arithmetic operations involving complex numbers, including squaring a binomial.
Binomial Expansion – Applying the binomial theorem to expand expressions of the form (a + b)^n.
Imaginary Unit – Recognizing that i^2 = -1 and correctly applying this in calculations.