Is there any conjugate for real numbers?

Yes, there is a conjugate of a real number. The real number 'a' is written as a+i(0)=a. We define the conjugate of x+iy as x-iy. Therefore, the conjugate of any real number 'a' is a-i(0)=a. read more

Well, the "real conjugate" is just the negative of the normal conjugate, $z\mapsto-\bar z$, so there's no lack of notation for it. – Akiva Weinberger Jan 12 '16 at 17: 08 Note that the product of a complex number and its complex conjugate is the exact opposite of the product of a complex number and its real conjugate. read more

Throughout this solution I will write z* for the complex conjugate of the complex number z. In particular, * in this answer is not multiplication. It is always the complex conjugate. There are two basic facts to remember: (1) If z is a complex number and |z| is the modulus of z, there is always a real number t with z = |z| e^(it). read more