SOLUTION: If z = icot(theata), show that (z+1)/(z-1)= cis(-2(theata))

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Question 187179: If z = icot(theata), show that (z+1)/(z-1)= cis(-2(theata))
Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!
How far do you get with this? I've just tried it and I can't spot any tricky or difficult bit, it's just complex algebra. Subtitute z=icot(theta) into the expression (z+1)(z-1), multiply by the complex conjugate of the denominator. Write everything in terms of sin and cos. It should come to cos^2 - sin^2 - 2isincos. Use the double angle formulas to see this is cos2 - isin2, then fiddle about with the minuses (cos -x = cos x, sin -x = -sin x) to get it into the exact form you want.