hw01 - j ) using (i) Cartesian forms; and (ii) polar forms,...

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ENEE 241 02 HOMEWORK ASSIGNMENT 1 Due Thu 02/05 Consider the complex numbers z 1 = - 3 + 4 j and z 2 = - 1 + 5 j (i) (2 pts.) Plot both numbers on the complex plane. (ii) (2 pts.) Evaluate | z i | and n z i for both values of i ( i = 1 , 2). (iii) (6 pts.) Express each of z 1 + 2 z 2 , z 1 - z 2 and z 1 z 2 in both Cartesian and polar form. (iv) (3 pts.) If v = z 4 1 · z 2 2 , determine | v | and n v without performing complex multiplications or divisions. Hence obtain v in Cartesian form. (v) (4 pts.) If w = z 5000 2 , determine n w in the range [0 , 2 π ). Your answer should be correct to four decimal places. (vi) (3 pts.) Determine b and c so that the quadratic polynomial t 2 + bt + c has roots z 1 and z 1 . Solved Examples S 1.1 ( P 1.9 in textbook). Simplify the complex fraction (1 + j 3)(1 - j ) ( 3 + j )(1 +
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Unformatted text preview: j ) using (i) Cartesian forms; and (ii) polar forms, throughout your calculation. S 1.2 Consider the complex number z = 1 + 2 j 3-jb Determine the value(s) of b for which (i) z is purely real; (ii) z is purely imaginary; (iii) z has modulus equal to 2 / 2. S 1.3 If z = (3 / 5) + j (9 / 10), express z 17 in polar form ( r, ), where [0 , 2 ). S 1.4 On the complex plane, sketch the curves given by the following equations: (i) | z-1 + j | = 1 (ii) | z-2 | = | z-3 j | Using geometry, determine the minimum value of | z | in each case (i.e., as z traces out each curve)....
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