Question

complex conjugate?

Answer 1

how do I know what \(r^*\) is?\[r=\frac{\cos{\theta_i}-i\sqrt{\sin^2{\theta_i}-n_{ti}^2}}{\cos{\theta_i}+i\sqrt{\sin^2{\theta_i}-n_{ti}^2}}\]

Answer 2

is it literally just flipping the numerator and denominator?

Answer 3

No. Your number in general terms, with a and b real, is
\[ r = \frac{a - bi}{a + bi} = \frac{ (a-bi)^2}{a^2 + b^2} = \frac{(a^2 - b^2) -2ab i}{a^2 + b^2} \]
Thus
\[ r* = \frac{(a^2 - b^2) +2ab i}{a^2 + b^2} \]