Tau and phi (conjugates?) fibonacci sequence

[vanmaiden]

Homework Statement

Would tau and phi be considered conjugates?

Homework Equations

$\tau$ = $\frac{1-\sqrt{5}}{2}$
$\phi$ = $\frac{1+\sqrt{5}}{2}$

The Attempt at a Solution

I know that a complex number such as 1+2i would have 1-2i as a conjugate. However, for fractions, I can't quite remember if the same rule applies.

Thank you in advance

 

[lanedance]

yes, the reason is tau x phi will give a results with not square roots in the expression

similarly for complex numbers, the result of multiplying conjugates is real

 

[vanmaiden]

yes, the reason is tau x phi will give a results with not square roots in the expression

similarly for complex numbers, the result of multiplying conjugates is real

Thank you! This will help me better understand the binet formula