If z = -2 + 2i, what is the value of |z|? (2019)

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Question: If z = -2 + 2i, what is the value of |z|? (2019)

Options:

Correct Answer: 2√2

Solution:

|z| = √((-2)^2 + (2)^2) = √(4 + 4) = √8 = 2√2.

If z = -2 + 2i, what is the value of |z|? (2019)

If z = -2 + 2i, what is the value of |z|? (2019)

Step 1: Identify the complex number z. Here, z = -2 + 2i.
Step 2: Recall the formula for the magnitude (or absolute value) of a complex number z = a + bi, which is |z| = √(a^2 + b^2).
Step 3: In our case, a = -2 and b = 2.
Step 4: Substitute a and b into the formula: |z| = √((-2)^2 + (2)^2).
Step 5: Calculate (-2)^2, which is 4.
Step 6: Calculate (2)^2, which is also 4.
Step 7: Add the results from Step 5 and Step 6: 4 + 4 = 8.
Step 8: Take the square root of 8: |z| = √8.
Step 9: Simplify √8 to 2√2.

Complex Numbers – Understanding the representation of complex numbers in the form a + bi and calculating their magnitude.
Magnitude of Complex Numbers – Using the formula |z| = √(a² + b²) to find the magnitude of a complex number.