Question

If \( z = 3 + 4i \), then the modulus of \( z \) is:

• A. \( 5 \)
• B. \( 7 \)
• C. \( 9 \)
• D. \( 10 \)

Hint:

To find the modulus of a complex number \( a + bi \), use the formula \( |z| = \sqrt{a^2 + b^2} \).

Answer 1

The Correct Option is A

We are given the complex number \( z = 3 + 4i \), and we need to find its modulus. Step 1: Recall the formula for the modulus of a complex number The modulus of a complex number \( z = a + bi \) is given by: \[ |z| = \sqrt{a^2 + b^2} \] Here, \( a = 3 \) and \( b = 4 \). Step 2: Calculate the modulus Substitute \( a = 3 \) and \( b = 4 \) into the formula: \[ |z| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \] Answer: The modulus of \( z \) is \( 5 \), so the correct answer is option (1).