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4C.NCN.3.1.12.6.11 2011 Domain: Number and Quantity Cluster: Perform arithmetic operations with complex numbers. Standards: 3. (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. Essential Questions Enduring Understandings How do you use conjugates? What is the relationship between conjugates and real numbers? What are real-life situations involving complex conjugates? Content Statements Students will find the conjugate of a complex number. Students will use conjugates to find moduli. Students will use conjugates to find quotients of complex numbers. Assessments Complex conjugates are number pairs of the form a + bi and a – bi. Modulus of a complex number is the distance of the number from the origin. To find the modulus of a complex number, take the square root of the product of the complex number and its conjugate. Quotients can be expressed as a fraction. Multiply the numerator and denominator by the complex conjugate of the denominator to obtain a real number in a denominator. Activities, Investigation, and Student Experiences 1. Activity: Using NSpire calculators to find quotients of complex numbers. http://education.ti.com/calculators/timathnspired/US/Act ivities/Detail?sa=1010&t=1179&id=10888 2. http://mathforum.org/mathtools/activity.html?id=818& From the Math Forum-A children's book-on-the-Web from Australia, designed to introduce complex numbers in story form in a way that is intuitive and enjoyable for students. 3. Evaluate the expression and write the result in the form a + bi. (2 3i)(5i) 2 3i 4C.NCN.3.1.12.6.11 2011 Students will answer short-answer questions, showing all work. For example: 1. Evaluate the expression 2i and write the result in the 4 3i form a + bi. 1 4 2. Evaluate the expression and write the results in 1 1 the form a + bi. 3. Use the complexconjugate to determine the modulus. 3 1 i 3 Equipment Needed: Teacher Resources: Smart board Calculators (graphing) White boards Overheads http://www.purplemath.com/modules/comple x2.htm http://www.khanacademy.org/video/complex -numbers--part-2?playlist=Algebra http://www.khanacademy.org/video/complex -numbers--part-1?playlist=Algebra http://www.mathworksheetsgo.com/algebracalculators/complex-numbercalculator.php http://education.ti.com/calculators/timathnspired/US/Activiti es/Detail?sa=1010&t=1179&id=10888 http://mathforum.org/mathtools/activity.html?id=818&