If $w = \dfrac{z+2}{z-2}$ then $w(z-2) = z+2$. Solve that for $z$ to get $z = \dfrac{2(1+w)}{w-1}.$ Now let $w = u+iv$, and find the real and imaginary parts of $\dfrac{2(1+w)}{w-1}$ in terms of $u$ and $v$. That way, you can find equations for the point $(u,v)$ in the $w$-plane corresponding to the lines Re$(z)$ = const. and Im$(z)$ = const.ob1st said:W= z+2 /z-2 drawing mapping find image in w plane line Re(z)constant and im(z)=constant find fixed point from mapping
A fixed point for a complex mapping is a point in the complex plane that does not change when the mapping is applied. In other words, the complex number representing the point remains the same after the mapping is performed.
To calculate a fixed point for a complex mapping, we set up an equation where the fixed point, represented by the complex number z, is equal to the mapping function, f(z), applied to that same fixed point. The solution to this equation is the fixed point.
Yes, a complex mapping can have zero, one, or multiple fixed points. This depends on the specific mapping function and the values of the complex numbers involved.
Fixed points in complex mappings play a crucial role in understanding the behavior of the mapping. They can help us identify patterns, symmetries, and other properties of the mapping, and can also be used to simplify calculations and proofs.
Fixed points of complex mappings have numerous applications in physics, engineering, computer science, and other fields. They can be used to model the behavior of physical systems, design efficient algorithms, and solve complex problems in various domains.