InterviewSolution
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InterviewSolution
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In the Argands plane what is the locus of `z(!=1)`such that `a rg{3/2((2z^2-5z+3)/(2z^2-z-2))}=(2pi)/3dot` |
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Answer» `arg{(3)/(2)((2z^(2)-5z+3)/(3z^(2)-z-2))}=(2pi)/(3)` or `arg{(3)/(2)((z-1)(2z-3))/((z-1)(3z+2))}=(2pi)/(3)` or `arg{(3)/(2)((2z-3)/(3z+2))}=(2pi)/(3)` or `arg((z-3//2)/(z+2//3))=(2pi)/(3)` Thus, locus of z is minor arc whose end point are `(3)/(2)` and `(-3)/(2)` and included angle is `(2pi)/(3).` |
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