Question

If a is real number then why $\overline{a}=a$

Answer 1

Let $z=a+ib$ be a complex number

Then $\overline{z}=a-ib$ is the conjugate of z.

If we make $b=0$ i.e imaginary part =$0$

So that z is a pure real number

Then $z=a$

and $\overline{z}=a$

Thus $z=\overline{z}$

For real numbers, the conjugate of no. is itself the number.

i.e $\overline{a}=a$