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Consider the complex numbers zi = 4-5, and z2 =-2+Tj (i) (2 pts.) Plot both numbers on the complex plane (ii) (2 pts.) Evaluate lZjl and L2i for both values of i (i = 1,2) (iii) (6 pts.) Express each of zit 322, + 222 and in both Cartesian and polar form (iv) (3 pts.) If v = . 221, determine lul and Lv. Also, obtain v in Cartesian form (v) (4 pts.) If w-z2000, determine Lu, in the range [0, 27). Your answer should be correct to four decimal places (vi) (3 pts.) Determine the only real values b and c so that +5z1 + c = 0 Problem 1B Throughout this problem, let u=V3+5 and u=-j (i) (2 pts.) Express each number in the form rei. 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 For what value of a is w purely real? (iii) (5 pts.) Determine the constant c such that u is a root of 9 Plot all roots of this equation on the complex plane. (iv) (3 pts.) Sketch the circle described by the equation 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 (vi) (3 pts.) At which points does the line intersect the real and imaginary axes? Problem 1C Consider the sinusoid 2(t) = Acos(S2t + ), where A > 0 and It is known that (-, ]. Time t is in seconds