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hw02 - ENEE 241 02 HOMEWORK ASSIGNMENT 2 Due Tue 02/10...

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ENEE 241 02* HOMEWORK ASSIGNMENT 2 Due Tue 02/10 Please turn in the two problems separately, with your name and section number on each sheet (or set of sheets). Problem 2A Do not use a calculator for this problem. Express your answers using square roots and/or fractional multiples of π . Throughout this problem, let u = - 3 + j and v = - 1 - j (i) (2 pts.) Express each number in the form re . Plot both numbers on the complex plane. (ii) (4 pts.) Let a be real. Determine, in terms of a , the real and imaginary parts of the complex number w = a + j u + v For what value(s) of a is w purely imaginary? (iii) (5 pts.) Determine the roots of the equation z 6 - v 2 = 0 and plot them on the complex plane. Are there any conjugate pairs among the roots? (iv) (3 pts.) Sketch the circle described by the equation | z - u | = 1 Determine the points of intersection (if any) of this circle and the two axes, real and imaginary. (v) (3 pts.) Sketch the line described by the equation | z - v | = | z | Where does this line intersect the two axes? What is the value of its slope?
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