If z = 2 + 2i, find the modulus of z.

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Question: If z = 2 + 2i, find the modulus of z.

Options:

Correct Answer: 2√2

Solution:

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

If z = 2 + 2i, find the modulus of z.

If z = 2 + 2i, find the modulus of z.

Step 1: Identify the complex number z. Here, z = 2 + 2i.
Step 2: Recall the formula for the modulus of a complex number z = a + bi, which is |z| = √(a^2 + b^2).
Step 3: Identify the real part (a) and the imaginary part (b) of z. In this case, a = 2 and b = 2.
Step 4: Substitute the values of a and b into the modulus formula: |z| = √(2^2 + 2^2).
Step 5: Calculate 2^2, which is 4. So, |z| = √(4 + 4).
Step 6: Add the results: 4 + 4 = 8. Now, |z| = √8.
Step 7: Simplify √8. This can be written as √(4 * 2) = √4 * √2 = 2√2.

Modulus of a Complex Number – The modulus of a complex number z = a + bi is calculated using the formula |z| = √(a^2 + b^2), where a is the real part and b is the imaginary part.