Problem
Find the magnitude of the complex number \( z = 3 + 4i \).
Solution
Step 1 ：The magnitude of a complex number \( z = a + bi \) is given by the formula \( |z| = \sqrt{a^2 + b^2} \).
Step 2 ：Substituting \( a = 3 \) and \( b = 4 \) into the formula, we get \( |z| = \sqrt{3^2 + 4^2} \).
Step 3 ：Solving the expression, we get \( |z| = \sqrt{9 + 16} \).
Step 4 ：Solving the expression, we get \( |z| = \sqrt{25} \).
