Answer
$\overline{z}\cdot\overline{w}=23+14i$
Work Step by Step
$z=3-4i$ $;$ $w=5+2i$
$\overline{z}\cdot\overline{w}$
Find the conjugates of both complex numbers by changing the sign of their imaginary parts:
$\overline{z}=3+4i$
$\overline{w}=5-2i$
Evaluate the product:
$\overline{z}\cdot\overline{w}=(3+4i)(5-2i)=15-6i+20i-8i^{2}=...$
Substitute $i^{2}$ by $-1$ and simplify:
$...=15-6i+20i-8(-1)=15+14i+8=23+14i$
