Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

[micromass]

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]

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?

pi/2, right?

 

[micromass]

pi/2, right?

Not really, because we can also have negative multiples. -i and -3i are also multiples.

 

[cooljosh2k2]

Not really, because we can also have negative multiples. -i and -3i are also multiples.

well, pi/2 for positive multiples of i or I am > 0, or -pi/2 for negative multiples of i, or I am < 0

 

[micromass]

Indeed! That's it!

 

[cooljosh2k2]

Indeed! That's it!

WOW! Thank you so much for helping and putting up with me!