HW1.solutions.v3

HW1.solutions.v3 - 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) and (d) Solutions (a) Since , and . Thus and . Therefore (b) Since and . , and . Thus . Be careful when computing the arctangent. ATAN2 will compute the Therefore 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 (d) Convert to Cartesian form, add, then convert back to polar, 2. 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. (a) Let , then and Thus (c) The claim is false. Let , then while . 3. Exercise B.12(a). The obvious solution is , and another solution is (verify and are not distinct since this). Find 2 other distinct solutions. Note that the represent the same location on the unit circle. We need to find solutions that satisfy . Equivalently, we look for solutions which yield distinct solutions , , , 4. Exercise 1.2‐1 (page 141) (a), (b), (c) (a) ‐24 (b) ‐15 ‐6 0 0 9 18 (c) 2 5 8 5. Exercise 1.2‐2 (d) We do this in two parts. Let and . Then This yields 0 2 3 6. Exercise 1.4‐1 (a) and (d) (a) 1 5 (d) 7 2 ‐2 4 7. Exercise 1.4‐2 (first figure only) is the line The left‐most part of . Thus , while the right‐most part of is the line ...
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