Re: Limit of a complex function with cubed conjugate
So when solving a complex limit with z-->0 I can write in polar form and make both z and r go to zero? I wasn't sure if the argument goes necessarily to zero when z does or only the modulus
Re: Limit of a complex function with cubed conjugate
Originally Posted by Phyba
So when solving a complex limit with z-->0 I can write in polar form and make both z and r go to zero? I wasn't sure if the argument goes necessarily to zero when z does or only the modulus
As $z \to 0$ the modulus goes to zero while the exponential part spins around the unit circle with magnitude 1. So the overall magnitude goes to 0.
Re: Limit of a complex function with cubed conjugate
Originally Posted by Phyba
So that means that arg(z) doesn't go to zero when z goes to zero, right? (I meant to say both theta and r earlier, I'm sorry)
in this case no. You can contrive things so both the modulus and the argument go to zero but in this case only the modulus does. Note that speaking of the argument of 0 is nonsensical as it can be any value.