## Precalculus: Mathematics for Calculus, 7th Edition

$z\cdot\overline{z}=25$
$z=3-4i$ $;$ $w=5+2i$ $z\cdot\overline{z}$ Multiply the complex number $z$ by its conjugate. To obtain the conjugate, change the sign of its imaginary part: $z\cdot\overline{z}=(3-4i)(3+4i)=3^{2}-(4i)^{2}=9-16i^{2}=...$ Substitute $i^{2}$ by $-1$ and simplify: $...=9-16(-1)=9+16=25$