The discussion focuses on calculating the argument of the complex expression Arg[(z-1)/(z+1)], where z is a point on the unit circle (|z|=1). It is established that Arg[(z-1)/(z+1)] equals π/2 when the imaginary part of z (Im(z)) is greater than 0, and -π/2 when Im(z) is less than 0. The participants derive this by expressing (z-1)/(z+1) in terms of its real and imaginary components and confirming that it is purely imaginary, leading to the conclusion about the argument's values.
PREREQUISITESStudents studying complex analysis, mathematicians interested in the properties of complex functions, and anyone seeking to understand the behavior of arguments in complex numbers.
micromass said:OK, now the \frac{2b}{2a+1} is just a real number, so we're dealing with a multiple of i.
So our value could be 3i, 4i, 6i or some other multiple of i. What is the argument of a multiple of i?
cooljosh2k2 said:pi/2, right?
micromass said:Not really, because we can also have negative multiples. -i and -3i are also multiples.
micromass said:Indeed! That's it!