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Bogrune
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Homework Statement
2.) Solve
x7=1
I am to solve for all the solutions to this polynomial, including the complex solutions using trigonometry. I'm supposed to plot my solutions on the unit circle, with the x-axis being the real axis, and the y-axis being the imaginary (or complex) axis.
Homework Equations
I'm supposed to use the following Identities to solve the equation: Rcis, meaning: R (real) times cosine + i(complex) sine.
cisn(θ)=cis(nθ)
The Attempt at a Solution
I've numbered my steps taken in order:
x7=1
1.)(Rcisθ)7=1
2.)Rcis(θ)7=1
3.)cis7(θ)=1
4.)cis(7θ)=1
5.)cos(7θ) + isin(7θ)=1 + i0
5a.) cos(7θ)=1
7θ= cos-1(1)
7θ= 0 + 2πn
5b.) sin(7θ)=0
7θ= sin-1(0)
And that's where I got stuck.
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