but is in the third quadrant since both x and y are negative
EDIT: For the second one, all real positive numbers are on the positive x axis. So in that case
I have two small problems with some Questions about Complex numbers I have been looking through
For the 1st one. I do not understand how they got to the value of 4/3*Pi
And secondly I do not understand why in one example he says that its cis(0+...), while in all examples I have done before that one I was told to use cis(Pi+...).
Thanks for your time
The point is that we are thinking of the complex number "a+ bi" as a point in the xy-plane. a+ bi corresponds to the point (a, b). In polar coordinates, since and , so that as long as x is not 0. Even for x= 0, since tan(\theta) goes to infinity as goes to and to negative infinity as goes to , we have or .
Since is the angle the line from (0, 0) to (a, b) makes with the positive real axis, you should be able to see, without any calculation that (1) for any positive real number, , (2) for any positive real number times i (like 2i or ) , (3) for any negative real number (or since we can add or subtract any multiple of and have the same position), (4) for any negative real number times i (like -2i or ) (or ).