If z is a complex number, show that the sum of z and its conjugate...

Given z is a complex number.
Let z=x+iy
We know that conjugate of a complex number is given by changing sign of imaginary part.
Conjugate of given complex number z will be:
z=x−iy
Now, sum of complex number z and its conjugate will be:
${\displaystyle z+\bar{z}=(x+iy)+(x-iy)=x+iy+x-iy=2x}$
Therefore, sum of z and it conjugate is real number.