Complex Function

[shermaine]

Hello,

I have got some doubts over here.
Why is the following answer 1 and -1?
lim x+j0 / x-j0 = 1
x->1,y=0


lim 0+jy/0-jy = -1
x->0,y=0

I'm confused here....
Any gd website that i can read on for understanding of complex function, complex integration , laplace transform
Pls advise.
Thanks.

 

[Optikon]

Hello,

I have got some doubts over here.
Why is the following answer 1 and -1?
lim x+j0 / x-j0 = 1
x->1,y=0


lim 0+jy/0-jy = -1
x->0,y=0

I'm confused here....
Any gd website that i can read on for understanding of complex function, complex integration , laplace transform
Pls advise.

The first one is trivial. j0 = 0 so lim(x->1) of (x+0/x-0) = 1. Just plug in x=1. (1+0)/(1-0) = 1

The second one you have lim(x->0) of jy/-jy and jy cancel leaving lim(x->0) of 1/-1 which equals -1

Thanks.

 

[shermaine]

it should be

lim x+j0/x-j0 =1
x-->0,y=0


lim
x=0,y-->0 0+jy/0-jy =-1


May i know what is it mean by x=0,y-->0 ?

 

[ljcox]

it should be

lim x+j0/x-j0 =1
x-->0,y=0


lim
x=0,y-->0 0+jy/0-jy =-1


May i know what is it mean by x=0,y-->0 ?

x=0,y-->0 means that x is equal to zero and y is approaching zero.

In your examples, it is trivial since lim (x+j0)/(x-j0) =1 for all x and lim
x=0,y-->0 (0+jy)/(0-jy) =-1 for all y. Note that the brackets are necessary.

In general, (a + jb)/(x + jy) = {(a + jb) (x - jy)}/(x^2 + y^2) this is called rationalising the denominator.

I'll leave it to you to do the multiplication of the two complex terms.

Len