hwB01 - √ 3(1-j √ 3 j(1 j using(i Cartesian forms...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 1 Due Fri 01/08 Consider the complex numbers z 1 = - 1 + j 3 and z 2 = 1 - j (i) (3 pts.) Plot both numbers on the complex plane. (ii) (3 pts.) Evaluate | z i | and 6 z i for both values of i ( i = 1 , 2). (iii) (6 pts.) Evaluate (a) z 3 1 , (b) z 2 2 , and (c) z 2 1 + 2 z 1 + 4. (iv) (3 pts.) If v = z 6 1 · z - 12 2 , determine | v | and 6 v without performing complex multiplications or divisions. Hence obtain v in Cartesian form. (v) (5 pts.) Plot the circle described by the equation | z - z 1 - z 2 | = | z 1 | . This circle intersects the imaginary axis at two points. Determine these points by setting z = jy and squaring both sides of the equation. At what point(s) does the circle intersect the real axis? Solved Examples S 1.1 ( P 1.9 in textbook). Simplify the complex fraction (1 + j
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Unformatted text preview: √ 3)(1-j ) ( √ 3 + j )(1 + 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,θ ), where θ ∈ [0 , 2 π ). 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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This note was uploaded on 03/21/2010 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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