Functions of a Complex Variable

[sunnybrarrd]

Hi guys. Please help me with this.

Consider the Mapping:

w = 1/(z-j)

questions:(1) Write z as a function of w.

(2) Express X and Y in terms of u and v.

(3) Find and describe the image of the line x = 1 under this mapping.

Homework Equations

--

w = u+jv
z = x+jy

The Attempt at a Solution

I don't understand the first question and have no idea of how to have it as a function of w. However I do understand from then onwards as to express in terms u and v.

 

[HallsofIvy]

It's strange that you should be working with complex number and not understand something from basic algebra.
$$w= \frac{1}{z- j}$$
$$z- j= \frac{1}{w}$$
$$z= \frac{1}{w}+ j$$

 

[sunnybrarrd]

Thank you.

That is really simple. Probably that is why i was confused as I did not thought it would be that simple.

Thanks a lot!