# Thread: Limits with complex varibles.

1. ## Limits with complex varibles.

I am having trouble with
Limit of $2x+iy^2$as z->2i

i set it up at lim 2x as x->0 + i lim y^2 as y->2. so i get 4i as my limit but when i plug 2i directly i get -4i... is this right because of how the complex plain is defined?? or am i completely wrong thinking the limit is 4i? any help would be awesome!

2. The first problem is that you have a function in terms of $x$ and $y$, but telling it to make $z$ go to a value.

What is $z$?

3. z = x+yi so w= 0+2i?

i thought that i would do $\displaystyle \lim_{z \to w}\2x+iy^2 = \lim_{\left(x,y\right) \to (0,2)} 2x + i \lim_{(x,y) \to (0,2)} y^2$

4. If you are evaluating $\lim_{(x, y) \to (0, 2)}(x + iy^2)$...

$\lim_{(x, y) \to (0, 2)}(x + iy^2) = 0 + i(2^2)$

$= 4i$.

5. Originally Posted by fizzle45
I am having trouble with
Limit of $2x+iy^2$as z->2i

i set it up at lim 2x as x->0 + i lim y^2 as y->2. so i get 4i as my limit but when i plug 2i directly i get -4i... is this right because of how the complex plain is defined?? or am i completely wrong thinking the limit is 4i? any help would be awesome!
The errror is that you plugged 2i in for y. z= 2i, not y. Writing z= x+ iy then z= 2i means y= 2, not 2i.