SOLUTION: If arg((z-w)/(z-w^2)) =0,then prove that re(z)=-1/2,where (w and w^2 are non real cube roots of unity)
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-> SOLUTION: If arg((z-w)/(z-w^2)) =0,then prove that re(z)=-1/2,where (w and w^2 are non real cube roots of unity)
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Question 540721
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If arg((z-w)/(z-w^2)) =0,then prove that re(z)=-1/2,where (w and w^2 are non real cube roots of unity)
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richard1234(7193)
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If the argument of some complex number is 0, then the number must be a positive real number. Also, the numerator (z - omega) can be set to zero. We have
Since we want
we set
.
