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HW1.spring.2008.SOLUTIONS - ECE 2704 Homework Number 1 1...

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Unformatted text preview: ECE 2704 Homework Number 1 1. Exercise B.2 (page 64), parts (a), (b), (c) Solutions (a) Since , and . Thus and . Therefore (b) Since and . , and . Thus Therefore . Be careful when computing the arctangent. ATAN2 will compute the correct result, but there is no standard definition of how to call this function. MATLAB's implementation is atan2(y,x), while Excel's is atan2(x,y). The angle for this exercise is computed . with MATLAB by (c) First compute the product, Then convert to polar form 2. Exercise B.4 (a) Solution Let . Then and note that . 3. Exercise B.6 (a) and (e): Either provide a proof that the claim is correct, or provide a counter example that shows that the claim is false. Solutions (a) Let , then and Thus (e) The claim is false. Let 4. Exercise B.7 (a), (b), (c), (d), (e), (f) Solutions (a) and (b) (c) (d) (e) the magnitude and angle, Thus (f) we compute . Thus 5. Let Solution 6. For any complex number , show that Solution Let , then which has unit magnitude. . and compute . . To express the product in Cartesian form, and and . . To express the difference in polar form, we compute , then while . . Thus . . Thus . ...
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