Question

lf $Z=3+2i$ then

$(Z+\overline{Z}{)}^2+(Z-\overline{Z}{)}^2-3Z\overline{Z}=$

• A. 0
• B. 95
• C. -19
• D. 85

Answer 1

Answer: (C)

-19

$z+\overline{z}=2Re\left(z\right)=2\times 3=6$

$z-\overline{z}=2iIm\left(z\right)=4i$

$z\overline{z}={\left|z\right|}^2=(\sqrt{3^2+2^2}{)}^2=13$

$\Rightarrow (z+\overline{z}{)}^2+(z-\overline{z}{)}^2-3z\overline{z}$

$=36-16-3\ast 13$

$=-19$