rickypontingdagoat
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Wanted to ask how to do this question.
In the argand diagram below, Point P lies in the first quadrant on the unit circle. P represents the complex number w and z=w is a root of z^5=1. anglePOx=theta
(I have not included the diagram, which is only a unit circle with a vector labelled P with argument theta)
these are the below parts to the question. I need help with part e, and im quite lost at how to use all these previous parts together to obtain this exact value
a) show that theta is equal to 72 degrees
b) show that 1+w+w^2+w^3+w^4=0
c) if a=w+w^4 and b=w^2+w^3 show that a+b=-1 and ab=-1
d) show that (a-b)^2=5
e) given a-b>0, find the exact value of cos72
Any help would be greatly appreciated.
In the argand diagram below, Point P lies in the first quadrant on the unit circle. P represents the complex number w and z=w is a root of z^5=1. anglePOx=theta
(I have not included the diagram, which is only a unit circle with a vector labelled P with argument theta)
these are the below parts to the question. I need help with part e, and im quite lost at how to use all these previous parts together to obtain this exact value
a) show that theta is equal to 72 degrees
b) show that 1+w+w^2+w^3+w^4=0
c) if a=w+w^4 and b=w^2+w^3 show that a+b=-1 and ab=-1
d) show that (a-b)^2=5
e) given a-b>0, find the exact value of cos72
Any help would be greatly appreciated.
