(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Used the definition of a limit to prove that as z=>0 lim (z bar)^2/(z)=0

2. Relevant equations

abs(f(z)-w(0)) < eplison whenever abs(z-z(0)) < lower case delta

3. The attempt at a solution

let z=x+iy and z bar = x-iy

z=(x,y)

Since limit of function is approaches origin, there are two cases when the limit approaches the origin: when (x,0) and when (y,0)

first case(real axis): z=>(x,0) lim (z bar)^2/(z)=0 => (x-i*0)^2/(x+i*0)=(x^2)/x= x

second case(imaginary axis) : z=>(0,y) lim (z bar)^2/(z)=0 => (0-i*y)^2/(0+i*y)=(i*y)^2/(i*y)= i*y

Both cases each time show that the function has two different limits, and that the limit of the function does not approach zero in either case.

So how can the limit of the function be zero?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Limit of a complex function

**Physics Forums | Science Articles, Homework Help, Discussion**