The discussion revolves around finding the arguments of the complex numbers -4-3i and -4+3i, focusing on the principles of complex analysis related to angle measurement in the complex plane.
Some participants affirm the original poster's approach while others suggest that visual aids, such as drawings, might help clarify the understanding of angles in the complex plane. The discussion reflects varying interpretations of angle reference frames.
There is mention of the principle of argument and its constraints, including the range of angles considered and the periodic nature of angle measurement in complex analysis.
Your prof. may have been referring to the fact that angles in the Complex plane depend on the "frame of reference" for angles, as well as to the periodicity. If , e.g., the x-axis corresponds to 0 , then you will have a certain angle, if you set the y-axis to be the 0 -reference, you will have another angle, etc. This relates to what is called a branch of the associated function of logarithm.Mathematicsss said:Homework Statement
What is the argument of -4-3i, and -4+3i?
Homework Equations
tantheta=opposite/adjacent side
The principle of argument is that the argument lies between -pi and pi (not including -pi).
The Attempt at a Solution
arg(-4-3i) = -pi + arctan(3/4)
arg(-4+3i) = pi - arctan(3/4)
My teacher wrote on the answer sheet that the argument of -4-3i is just arctan(3/4).. am I incorrect in the above arguments?[/B]