The complex number \( z = 3 + 4i \) is provided. The objective is to determine its modulus.
Step 1: Modulus Formula Reminder
The modulus of a complex number \( z = a + bi \) is defined as:
\[
|z| = \sqrt{a^2 + b^2}
\]
In this case, \( a = 3 \) and \( b = 4 \).
Step 2: Modulus Calculation
Substituting \( a = 3 \) and \( b = 4 \) into the formula yields:
\[
|z| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\]
Answer: The modulus of \( z \) is \( 5 \). Therefore, option (1) is the correct choice.
Was this answer helpful?
1
Top Questions on Complex Numbers and Quadratic Equations