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Solve cos( 4 θ ) = -1 .
There actually isn't too much to do along with this problem. However, it is different from all the others done to this point. All the others done to this point have had two angles in the interval [0, 2 θ ] which were solutions to the equation. it merely has one. Following is the solution to this equation.
4 θ = ? + 2 ? n ⇒ θ= ∏ /4 + ∏n/4 n= 0, ±1, ±2,..........
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is 1 and 1/2+2 and 1/7 3 and 9/4
(19 + 7 i)
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