show roots of eqn [(2+z)/(2-z)]^5 = 1 are 2itan(kpi/5) where k=0, +1, -1, +2, -2

[kevin123]

i. Prove [cos(x)+isin(x)-1]/[cos(x)+isin(x)+1] = itan(x/2)

I've proved this part already

ii. Find all the roots of w^5 = 1

Done

iii. Show that roots of the equation

[ ( 2 + z ) / ( 2 - z ) ]^5 = 1

are of the form 2i tan(k pi/5), where k = 0, +1, -1, +2, and -2

 

[stapel]

i. Prove [cos(x)+isin(x)-1]/[cos(x)+isin(x)+1] = itan(x/2)

I've proved this part already

ii. Find all the roots of w^5 = 1

Done

iii. Show that roots of the equation

[ ( 2 + z ) / ( 2 - z ) ]^5 = 1

are of the form 2i tan(k pi/5), where k = 0, +1, -1, +2, and -2

How have you tried to use the first two parts of this in solve the third? Please reply showing your efforts so far. Thank you!