How to prove that if (z+1)/(z-1) = ki then |z| = 1

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If |z|=1 and w=(z-1)/(z+1) where z not equal to -1 then the value of Re(w) will be what...? If |z|=1 and w=(z-1)/(z+1) where z not equal to -1 then the value of Re(w) will be what...?
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If `sin^-1x+sin^-1y+sin^-1z=pi` prove that (1)`xsqrt(1-x^2)+ysqrt(1-y^2)+zsqrt(1-z^2)=2xyz` If `sin^-1x+sin^-1y+sin^-1z=pi` prove that (1)`xsqrt(1-x^2)+ysqrt(1-y^2)+zsqrt(1-z^2)=2xyz`
If a^ x =b,b^ y =c,c ^z =a then show that xyz=1. If a^ x =b,b^ y =c,c ^z =a then show that xyz=1.
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if sin^-1x+sin^-1y+sin^-1z=π then prove that x√1-x^2+y√1-y^2+z√1-z^2=2xyz if sin^-1x+sin^-1y+sin^-1z=π then prove that x√1-x^2+y√1-y^2+z√1-z^2=2xyz
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