Question

Adding an irrational number with its conjugate is:

• A. always a rational number
• B. always an irrational
• C. either rational or irrational
• D. always an integer

Answer 1

The correct option is A always a rational number

Adding an irrational number with its conjugate is always a rational number.

Because the irrational parts are equal and opposite (in terms of sign) in the conjugates and as we add them they get cancelled.

Conjugates are of the form $R\pm I$, where $R=$ real part, and $I=$ imaginary part.

An adding, $(R+I)+(R-I)=2R$, which is rational.