The discussion revolves around the argument of a complex number expressed in polar form, specifically for the complex number (1/√2) - (i/√2). Participants are examining the differences in the calculated arguments and their representation in different quadrants.
The discussion is ongoing, with participants exploring the reasoning behind the different representations of the argument. Some guidance is provided regarding the definition of the principal argument, but no consensus has been reached on the correctness of the initial calculations.
There is a mention of the principal argument being defined within the range of (-π, π], which may influence the interpretation of the results. Participants are also reflecting on the quadrant placement of the angles involved.
charmedbeauty said:Homework Statement
express the arg(z) and polar form of
(1/\sqrt{2}) - (i/\sqrt{2})
Homework Equations
The Attempt at a Solution
Ok so I did \sqrt{(1/\sqrt{2})^{2}+(1/\sqrt{2})^{2}} = 1
so tan^{-1}(1) = \pi/4 so arg(z)=5\pi/4
but they had the answer as -3\pi/4
Am I wrong or are they because shouldn't the arg(z) lie in the third quad.??