# Complex Mapping - Express x & y in terms of u & v

• evermore
In summary, the conversation discusses the expression of w and z in terms of u, v, x, and y. It mentions the use of substitution to simplify the equation and the next steps involve separating the equation into real and imaginary parts. The conversation concludes with a humorous comment about engineers and their use of "j" for imaginary numbers.
evermore
w = 1/(z+2j): w = u + jv, z = x+jy

Its not hard to express this in terms of z... z = 1/w - 2j
But how can i go about expressing x and y and terms of u and v
Substitution of those above terms gets you

x + jy = 1/(u + jv) - 2j

I am not clear on the next steps
Any help is much appreciated.
Thankyou

evermore said:
w = 1/(z+2j): w = u + jv, z = x+jy

Its not hard to express this in terms of z... z = 1/w - 2j
But how can i go about expressing x and y and terms of u and v
Substitution of those above terms gets you

x + jy = 1/(u + jv) - 2j

I am not clear on the next steps
Any help is much appreciated.
Thankyou
Get that fraction into a+ jb form by multiplying numerator and denominator by the complex conjugate of u+ jv:
x+ jy= (u- jv)/(u2+ v2)- 2j

Now separate into real and imaginary parts:
x= u/(u^2+ v^2), y= -v/(u^2+ v^2)- 2.

(I can't tell you how much it hurt to write "j" instead of "i". Blast these engineers and their jmaginary numbers!)

We are the infamous Electrjcal Engjneers..

## What is complex mapping?

Complex mapping is a mathematical concept that involves transforming a complex plane into another complex plane using functions. This allows us to represent complex numbers in terms of other variables, such as u and v.

## Why do we use complex mapping?

Complex mapping is used to simplify complex equations and make them easier to solve. It also allows us to visualize and understand complex functions in a more accessible way.

## How do we express x and y in terms of u and v?

We can use inverse functions to express x and y in terms of u and v. For example, if we have a function f(u,v) that maps to (x, y), we can use the inverse function to find the values of x and y in terms of u and v.

## What are some common functions used in complex mapping?

Some common functions used in complex mapping include logarithmic, exponential, and trigonometric functions. These functions help us to transform the complex plane and express variables in terms of u and v.

## How is complex mapping used in real-world applications?

Complex mapping is used in various fields, such as engineering, physics, and economics. It can help in solving complex equations and understanding complex systems. Additionally, it is used in computer graphics to create 3D models and animations.

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