Complex Numbers

Easymathematics

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

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√7

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Subject: mathematics
Chapter: complex numbers and quadratic equations
Topic: complex numbers
Difficulty: Easy
Year: 2025

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

This easy difficulty mathematics question is from the chapter complex numbers and quadratic equations, covering the topic of complex numbers. It appeared in the 2025 exam.

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