Help with these two problems in complex analysis

[Mathematicsss]

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]

 

[andrewkirk]

You are correct.

 

[scottdave]

Drawing a picture also will help you figure out an approximate angle, to see if you figured it correctly.

 

[WWGD]

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]

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.