What is the magnitude of the complex number $z=3-4i$?

Step-by-step solution

1. Identify the real part $a=3$ and the imaginary part $b=-4$ of the complex number.
2. Use the definition of magnitude: $|z|=\sqrt{a^2+b^2}$.
3. Compute $a^2+b^2=3^2+(-4{)}^2=9+16=25$.
4. Take the square root: $\sqrt{25}=5$.
5. Therefore, the magnitude of $z$ is $5$.

Concept tested: Magnitude of a complex number

Published 16 October 2026 · How this solution was prepared and checked