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Exploring Real and Complex Zeros of Functions

This lesson series focuses on helping students establish bounds for the real zeros of functions and identify potential rational zeros. The curriculum includes bell ringers, homework assignments, and exit tickets that reinforce these concepts. Students will also learn to perform operations with complex numbers, including using complex conjugates for division. Emphasis is placed on collaborative learning through peer grading and group discussions. Students are reminded to complete missing assignments and stay on track with their grades.

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Exploring Real and Complex Zeros of Functions

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  1. Date: 1/23/12 Objective: SWBAT establish bounds for the real zeros of a function & identify potential rational zeros. Bell Ringer: pg 218 #50 HW Requests: Go over problems from worksheet Exit Ticket: (p. 217-17 #33, 35, 37, 41, 45, 47, 49, 51) Homework: Complete Rational Zeros Worksheet (Graded) Start p. 217 #38-56 evens and 62 - Absent must complete worksheet Announcements: 2 missing assignments no later than Tues. 1/24/12

  2. Upper and Lower Bound Tests for Real Zeros

  3. Date: 1/24/12 Objective: SWBAT establish bounds for the real zeros of a function & identify potential rational zeros. Bell Ringer: pg 217 #38,42 HW Requests: Go over problems from worksheet Exit Ticket: 51, 53, 55 Homework: p. 217 #38-56 evens and 62 Absent must complete worksheet Announcements: Check Grades

  4. Date: 1/25/12 Objective: SWBAT perform operations with complex numbers. Bell Ringer: Quick Review #10 HW Requests: Stamp HW p. 217 #38-56 evens and 62 – Turn in Worksheet Go over problems from worksheet Peer Graded Homework: pg 227 #1-19 odds, 29, 31 Announcements: Check Grades!

  5. Date: 1/26/12 Objective: SWBAT perform operations with complex numbers. Bell Ringer: pg 226 #26 HW Requests: pg227 #1-19 odds, 29, 31 Homework: pg227 #24-27, 33-51 odds Announcements: Check Grades!

  6. Complex Conjugates and Division Complex conjugates-a pair of complex numbers of the form a + bi and a – bi where a and b are real numbers. ( a + bi )( a – bi ) a 2 – abi + abi – b 2 i2 a 2 – b 2( -1 ) a 2 + b 2 The product of a complex conjugate pair is a positive real number.

  7. Complex Conjugate

  8. To find the quotient of two complex numbers multiply the numerator and denominator by the conjugate of the denominator.

  9. Perform the operation and write the result in standard form.

  10. Perform the operation and write the result in standard form.

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