If z1 = 2 + 2i and z2 = 2 - 2i, what is the value of z1 * z2? (2019)

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Question: If z1 = 2 + 2i and z2 = 2 - 2i, what is the value of z1 * z2? (2019)

Options:

Correct Answer: 8

Exam Year: 2019

Solution:

z1 * z2 = (2 + 2i)(2 - 2i) = 4 - 4i^2 = 4 + 4 = 8.

If z1 = 2 + 2i and z2 = 2 - 2i, what is the value of z1 * z2? (2019)

If z1 = 2 + 2i and z2 = 2 - 2i, what is the value of z1 * z2? (2019)

Step 1: Identify the complex numbers. Here, z1 = 2 + 2i and z2 = 2 - 2i.
Step 2: Write down the multiplication of the two complex numbers: z1 * z2 = (2 + 2i)(2 - 2i).
Step 3: Use the formula for multiplying two binomials: (a + b)(c - d) = ac - ad + bc - bd.
Step 4: Apply the formula: (2)(2) + (2)(-2i) + (2i)(2) + (2i)(-2i).
Step 5: Calculate each part: 2 * 2 = 4, 2 * -2i = -4i, 2i * 2 = 4i, 2i * -2i = -4i^2.
Step 6: Combine the results: 4 - 4i + 4i - 4i^2.
Step 7: Notice that -4i and +4i cancel each other out: 4 - 4i + 4i = 4.
Step 8: Remember that i^2 = -1, so -4i^2 becomes +4: -4i^2 = 4.
Step 9: Add the results together: 4 + 4 = 8.
Step 10: Conclude that the value of z1 * z2 is 8.

Complex Number Multiplication – The question tests the ability to multiply two complex numbers using the distributive property and the fact that i^2 = -1.