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

AI Thread Summary
To solve for U and V in the equation U - iV = ln((z - 1)/(z + 1)), where z = x + iy, one approach is to express (z + 1)/(z - 1) in the form A + Bi, identifying the real part A and the imaginary part B. After obtaining A and B, converting to polar form can simplify the process. The discussion highlights challenges faced in manipulating the equation, specifically with exponential forms and polar coordinates. Participants suggest focusing on expressing the fraction in a suitable format before applying logarithmic properties. This method is essential for determining the real and imaginary components accurately.
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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.
 
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First write (z+1)/(z-1) in the form A+Bi where A and B are real. Then convert that to the polar form.
 
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