I'm working out an impedance matching problem from a textbook (it is not part of any coursework) and I am trying to figure out how they get the 315 term in the polar coordinates below. Z = (XC*RL)/(XC+RL) = (-j333*(1000))/(-j333+1000) = 315 , -71.58* = 100 -j300 ohms I calculated that atan(1000/-333) = 71.58* however I do not understand where they got the 315 from. I get 249 or 499 depending on positive or negative. I understand that 315 would be the length of the ray, and -71.58 would be the angle as this is capacitive hence -j. e.g. converting from rectangular to polar if I understand correctly. It was explained as (333*1000)/(sqrt(333^2+1000^2)) and that indeed does give us 315.943 ~316, however, I do not understand how they used the mathematical function to get to this point and I was hoping someone could explain what I'm missing.