Solve Matrix Proof: Q36 + Bonus Q38

[Gameowner]

Homework Statement

Questions on it's own are relatively simple, however, there is a bonus question which asks ''with a right choice of Theta, show how you can do question 36 easily with question 38''

Homework Equations

The Attempt at a Solution

Attempting question 36, it is known that B^8 is the identity matrix, so B^2001 is I*B.

Question 38 is just using some product to sum formulas etc, but I'm stuck as to how I apply question 38 to solve 36? my initial guess is Theta=pi or pi/2?

Any hints, tips would be much appreciated.

 

[lanedance]

so try and find an angle \theta such that A(\theta) = B

A is a rotation matrix, and aplying A^2 rotates by twice the angle, so have a think what 2001 times the angle is for B