If `alpha` is a root of `x^4 = 1` with negative principal argument then the principal argument of `Delta(alpha) = |(1,1,1), (alpha^n, alpha^(n+1), alp

Monjur Alahi

If `alpha` is a root of `x^4 = 1` with negative principal argument then the principal argument of `Delta(alpha) = |(1,1,1), (alpha^n, alpha^(n+1), alpha^(n+3)), (1/alpha^(n+1), 1/alpha^n, 0)|` is
A. `(5pi)/(14)`
B. `-(3pi)/(4)`
C. `(pi)/(4)`
D. `-(pi)/(4)`


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Salim Ahmed Kawsar

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Correct Answer - B
`(b)` Clearly `alpha=-i` where `i^(2)=-1`
So `Delta(alpha)=0+alpha^(2)+1-1-0-alpha^(3)`
`=(-i)^(2)+1-1-(-i)^(3)`
=-1+1-1-i=-1-i`
So, principal argument of `Delta(alpha)` is `-(3pi)/(4)`.

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