Track / Stage 4 / 158 of 340 #418 of 1964

Given $(a+b i)^{2}=3+4 i$, where $a, b \in \mathbf{R}, i$ is the imaginary unit, then the value of $a^{2}+b^{2}$ is $\qquad$

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Official solution

Answer 5.
Analysis From $(a+b i)^{2}=3+4 i$ we get $|a+b i|^{2}=|3+4 i|$, which means $a^{2}+b^{2}=5$.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.