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

Question 187179: If z = icot(theata), show that (z+1)/(z-1)= cis(-2(theata))
Answer by kev82(151) (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.
RELATED QUESTIONS
If tan theata =1 then find sin theata �cos... (answered by KMST)

find cos of theata if csc of theata is -2 and cos of theata... (answered by stanbon)

1. if sin of theata is < 0 and tha of theata is < 0 which quadrant is it in. (answered by ikleyn)

Consider {{{z^5-i=0}}} By finding the roots in cis{{{theta}}} form, and using... (answered by MathLover1,ikleyn)

Find z_1z_2 in polar form. z_1 = 4 cis(110°); z_2 =... (answered by greenestamps)

(z+1)/(z-1) = ki show that z*zbar... (answered by tommyt3rd)

If (x + 1/x) = 1 and (z + 1/z) =1; show that (z + 1/x)... (answered by robertb)

if |(z)/(|conj(z)|) -conj(z) | = 1 + | z | , z \[Element] C , then (z imaginary) prove... (answered by Edwin McCravy,ikleyn)

prove that ,if |(z)/(|conj(z)|) -conj(z) | = 1 + | z | , z \[Element] C , then (z... (answered by ikleyn)