I just had a question involving both psi and phi. I know that: Ψ= (1-√5)/2 = -0.618033989... Φ= (1+√5)/2 = 1.618033989... And out of boredom, I decided to put into my calculator: (Φ^Ψ) = 0.7427429446... But my question rose from there: What happens if you do (Ψ^Φ)? I plugged it in and got ERR:Nonreal Ans and couldn't distinguish why that had happened. So, I went to my math teacher and he had no idea. I then went to my statistics teacher and he had said the only way he could see an error was some sort of correlation involving squaring a negative number, which may have some similarity with taking the square root of a negative number as well. To see if he was right, I tested: (-√(5))^(√(5)) To get the same error. My question is, why does this happen and what exactly is this error?