Complex Numbers

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If z = 3 + 4i, then |z| equals

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1. **Modulus Definition**: For any complex number $z = a + bi$, the modulus (absolute value) is defined as $|z| = \sqrt{a^2 + b^2}$.
2. **Identify Components**: Here, $a = 3$ (real part) and $b = 4$ (imaginary part).
3. **Calculation**:
   - $|z| = \sqrt{3^2 + 4^2}$
   - $|z| = \sqrt{9 + 16} = \sqrt{25}$
4. **Result**: $|z| = 5$. Geometrically, this is the distance of the point $(3, 4)$ from the origin in the Argand plane.

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