This one follows on from the question I just asked about logarithms.. Turns out 1/x questions confuse me (sorry for bombarding your exchange with questions, this isn't homework or anything I am just trying to understand stuff)
Okay so I am trying to work out the phase of the following complex number 1/jw
My usual method would be to plot this on an Argand diagram and then take the inverse tangent to get the angle
So as an example if the number was 5+2jw this would be tan^-1(imag/real) = tan^-1(2/5)
However with 1/jw there is no real and the imaginary is 1/jw so I would attempt the same thing imag/real which is (1/jw)/0 =infinity.. Tan^-1(infinity) =90.. So why does Matlab tell me the answer is -90??
Ps I am very sorry for not using formatting I am on my ipad and also am not sure how to do it..
Best Answer
Take into acount that:
$$z = 1/j = j/j^2 = - j = 1|_{-\pi/2}.$$
If you actually want to obtain the phase of the complex number through the "tangent method", then:
$$\alpha = \arctan(\text{Im}(z)/\text{Re}(z)) = \arctan(-\infty) = - \pi/2.$$
Cheers!