## College Algebra 7th Edition

We are given that $z=a+bi$: $z\cdot\overline{z}=(a+bi)\cdot\overline{(a+bi)}=(a+bi)(a-bi)=a^{2}-abi+abi-b^{2}i^{2}=a^{2}+b^{2}$ We know that $a$ and $b$ are real numbers, so $a^2+b^2$ is a real number.