Show that ((√7 + i√3)/(√7 -i√3) + (√7 - i√3)/(√7 + i√3)) is real.

Question

Show that \(\left({\frac{\sqrt7+i\sqrt3}{\sqrt7-i\sqrt3}}+\frac{√7-i√3}{√7+i√3}\right)\)

((√7 + i√3)/(√7 -i√3) + (√7 - i√3)/(√7 + i√3)) is real.

Answer 1

\(\left({\frac{\sqrt7+i\sqrt3}{\sqrt7-i\sqrt3}}+\frac{√7-i√3}{√7+i√3}\right)\)

= 8/10 = 4/5, 

which is real.