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Exercise 1.1 · Q14

Q.State whether the following sentence is a statement. Justify your answer. In case it is a statement, state its truth value: The sum of cube roots of unity is zero.

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"The sum of cube roots of unity is zero" is a declarative mathematical claim, hence a statement.

The cube roots of unity are the roots of x3=1x^3=1, namely 1,ω,ω21, \omega, \omega^2, where ω=−1+i32\omega=\tfrac{-1+i\sqrt3}{2}. They satisfy 1+ω+ω2=01+\omega+\omega^2=0 (this follows from x3−1=(x−1)(x2+x+1)=0x^3-1=(x-1)(x^2+x+1)=0, and the sum of roots of x2+x+1=0x^2+x+1=0 is …

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