For each part of this problem, you must determine all distinct complex numbers s that are...

    

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For each part of this problem, you must determine all distinct complex numbers s that are solutions of the given equation. Solutions are distinct if they occupy different loca- tions in the complex plane. Express all solutions in both rectangular and exponential forms. Then sketch all of the solutions to that equation, by marking each location with an X, using one pair of axes for each equation. You are encouraged to use MATLAB, e.g. the roots function, to help you find solu- tions, but you must provide hand-written solutions that prove your answers are true, and sketch the solutions by hand on labeled axes. Some classical techniques that may be useful are: DeCartes' rule of signs, the quadratic formula, the rational root theorem, and its corollary, the integer root theorem. (a) All complex numbers s that are solutions to where B3(s) is the polynomial B3(s). B3(-s) = 0, B3(s) 83+2s2+2s+1. = (b) All complex numbers s that are solutions to PK(s) s+(K-1)s+ (3K-2) = 0, == where K can take any value in the set KE {0, 1, 5, 9, 13, 14}. For each part of this problem, you must determine all distinct complex numbers s that are solutions of the given equation. Solutions are distinct if they occupy different loca- tions in the complex plane. Express all solutions in both rectangular and exponential forms. Then sketch all of the solutions to that equation, by marking each location with an X, using one pair of axes for each equation. You are encouraged to use MATLAB, e.g. the roots function, to help you find solu- tions, but you must provide hand-written solutions that prove your answers are true, and sketch the solutions by hand on labeled axes. Some classical techniques that may be useful are: DeCartes' rule of signs, the quadratic formula, the rational root theorem, and its corollary, the integer root theorem. (a) All complex numbers s that are solutions to where B3(s) is the polynomial B3(s). B3(-s) = 0, B3(s) 83+2s2+2s+1. = (b) All complex numbers s that are solutions to PK(s) s+(K-1)s+ (3K-2) = 0, == where K can take any value in the set KE {0, 1, 5, 9, 13, 14}.