Question

If $z$ is a complex number satisfying $z-12=i(9-2\overline{z}),$ then the value of $z+\overline{z}$ is

• A. $10$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is B $4$

Given equation is $z-12=i(9-2\overline{z})$
Let $z=a+ib$
Now,
$z-12=i(9-2\overline{z})\Rightarrow z+2i\overline{z}=12+9i\Rightarrow (a+ib)+2i(a-ib)=12+9i\Rightarrow (a+2b)+i(b+2a)=12+9i\Rightarrow a+2b=12,b+2a=9\Rightarrow a=2,b=5\Rightarrow z=2+5i\therefore z+\overline{z}=2Re\left(z\right)=4$