How Do You Solve for U and V in the Complex Equation U-i*V=ln((z-1)/(z+1))?

[delolean]

Homework Statement

U-i*V=ln((z-1)/(z+1)) - solve for U and V, where U is the real part and V is the imaginary part, of this equation

Homework Equations

z=x+i*y, where x and y are the real and imaginary parts respectively

The Attempt at a Solution

I've attempted raising it to the power e, but that didn't help, I also tried z=r*exp(i*theta) but that didn't seem too help much. I'm really stuck on this one. Thanks.

 

[Dick]

First write (z+1)/(z-1) in the form A+Bi where A and B are real. Then convert that to the polar form.

 

[Architeuthis Dux]

I would approach this problem by first recognizing that the equation is in the form of a complex logarithm, where the argument is a complex number. Therefore, I would use the properties of logarithms to simplify the equation and isolate the complex number z on one side. This would involve taking the natural logarithm of both sides and using the properties of logarithms to rewrite the right side of the equation.

Once z is isolated, I would then use the definition of a complex number, z=x+iy, to equate the real and imaginary parts of the equation. This would result in two equations, one for the real part and one for the imaginary part, which can be solved simultaneously to find the values of U and V.

Additionally, I would also consider using the polar form of a complex number, z=r*exp(i*theta), to simplify the equation and possibly make it easier to solve.

In conclusion, solving this equation for U and V may require some algebraic manipulation and the use of logarithm and complex number properties. It may also be helpful to consider alternate forms of complex numbers, such as the polar form, to simplify the equation and make it easier to solve.