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

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

Correct Answer: 2i

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.

Complex Numbers – Understanding the properties and operations involving complex numbers, including addition, multiplication, and the use of the imaginary unit i.
Squaring a Binomial – Applying the formula (a + b)^2 = a^2 + 2ab + b^2 to expand the square of a complex number.
Imaginary Unit – Recognizing that i^2 = -1 and correctly applying this in calculations involving complex numbers.