# HW1 - THE UNIVERSITY OF TEXAS AT AUSTIN Dept of Electrical...

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THE UNIVERSITY OF TEXAS AT AUSTIN Dept. of Electrical and Computer Engineering EE313 Linear Systems and Signals HW1 Due: 02/01/2010 Problem 1.1 Properties of Complex Numbers Given that z 1 = r1e jθ1 and z 2 = r2 e jθ2 express the following operations in terms of r1, θ1, r2, and θ2 and simplify as much as possible. (a) z 1 * (b) z 2 2 (c) z 1 / z 2 (d) z 1 +z 1 * e)z1-jz1 * f)z1z1 * Part II: Double check your simplifications by using z1 = -3 +4j and z2 = 1 + 2j. This might be a good opportunity to write a Matlab script to compare the original expression with the simplified expression for each case above. In comparing numeric calculations for the original “o”and simplifed “s” expressions, you can consider them equal if i.e that the relative error is less than 10 -10 . Hint: Be careful when converting a complex number in Cartesian form to polar form. Getting the right quadrant of the angle is important. In order to compute the angle for a complex number x+jy, you could use ArcTan[x, y] in Mathematica or atan2(y, x) in Matlab. When writing a number in polar form, one format is to use Ae

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HW1 - THE UNIVERSITY OF TEXAS AT AUSTIN Dept of Electrical...

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