If z = 3 + 4i, find |z|.

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Question: If z = 3 + 4i, find |z|.

Options:

Correct Answer: 5

Solution:

The modulus |z| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

If z = 3 + 4i, find |z|.

If z = 3 + 4i, find |z|.

Correct Answer: 5

Step 1: Identify the complex number z, which is given as z = 3 + 4i.
Step 2: Recognize that the modulus |z| is calculated using the formula |z| = √(a^2 + b^2), where a is the real part and b is the imaginary part.
Step 3: In our case, a = 3 and b = 4.
Step 4: Substitute the values into the formula: |z| = √(3^2 + 4^2).
Step 5: Calculate 3^2, which is 9.
Step 6: Calculate 4^2, which is 16.
Step 7: Add the results from Step 5 and Step 6: 9 + 16 = 25.
Step 8: Take the square root of 25: √25 = 5.
Step 9: Conclude that the modulus |z| = 5.

Complex Numbers – Understanding the representation of complex numbers in the form a + bi, where a is the real part and b is the imaginary part.
Modulus of a Complex Number – Calculating the modulus (or absolute value) of a complex number using the formula |z| = √(a^2 + b^2).