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Transcript
A Practice Understanding Task – Sample Answers In order to find solutions to all quadratic equations, we have had to extend the number system to include complex numbers. " 2013(www.flickr.com/photos/milongadas( iNumbers Do the following for each of the problems below: Choose the best word [always, sometimes, never] to complete each conjecture. After you have made a conjecture, create at least four examples to show why your conjecture is true. If you find a counter-example, change your conjecture to fit your work. Conjecture #1: The sum of two integers is [always, sometimes, never] an integer. Answers will vary. Conjecture #2: The sum of two rational numbers is [always, sometimes, never] a rational number. Answers will vary. Conjecture #3: The sum of two irrational numbers is [always, sometimes, never] an irrational number. Answers may vary. Consider: 10 ( 10) 0 Conjecture #4: The sum of two real numbers is [always, sometimes, never] a real number. Answers will vary. Adapted from the Mathematics Vision Project Page 1 of 2 Conjecture #5: The sum of two complex numbers is [always, sometimes, never] a complex number. Answers will vary. Conjecture #6: The product of two integers is [always, sometimes, never] an integer. Answers will vary. Conjecture #7: The product of two rational numbers is [always, sometimes, never] a rational number. Answers will vary. Conjecture #8: The product of two irrational numbers is [always, sometimes, never] an irrational number. Answers will vary. Consider: 10 10 10 Conjecture #9: The product of two complex numbers is [always, sometimes, never] a complex number. Answers will vary. Conjecture #10: The product of two complex numbers is [always, sometimes, never] a real number. Answers will vary. Consider: (2 3i)(2 3i) 13 Conjecture #11: The product of two real numbers is [always, sometimes, never] a real number. Answers will vary. Conjecture #12: The product of two pure imaginary numbers is [always, sometimes, never] a real number. Answers will vary. Adapted from the Mathematics Vision Project Page 2 of 2