University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

379

Pages:

6
Author:

Amiah Sosa

Complex Numbers For use with Exploration 3.2 Essential Question What are the subsets of the set of complex numbers? Complex Numbers Imaginary Numbers Real Numbers Rational Numbers Integers Irrational Numbers Natural Numbers The imaginary unit i is defined as 2 Whole Numbers EXPLORATION: Classifying Numbers Work with a partner. Determine which subsets of the set of complex numbers contain each number. Notetaking with Vocabulary For use after Lesson 3.2 In your own words, write the meaning of each vocabulary term. • imaginary unit complex number pure imaginary number imaginary number Core Concepts The Square Root of a Negative Number Property 1. If r is a positive real number, then 2. By the first property, it follows that l "-/ r J 52 Algebra 2 r,J:_ S Complex Numbers (continued) EXPLORATION: Complex Solutions of Quadratic Equations Work with a partner. Use the definition of the imaginary unit i to match each quadratic equation with its complex solution. Justify your answers. a. Communicate Your Answer 3. What are the subsets of the set of complex numbers? Give an example of a number in each subset. 4. Is it possible for a number to be both whole and natural? natural and rational? rational and irrational? real and imaginary? Explain your reasoning. _ Algebra 2 51 Notetaking with Vocabulary (continued) Sums and Differences of Complex Numbers To add (or subtract) two complex numbers, add (or subtract) their real parts and their imaginary parts separately. Sum of complex numbers: Difference of complex numbers: (a + bi) - (e + di) ('.a+ bi) + fC + di) = (a+ c) + (b + d)i Extra Practice In Exercises 1-6, find the square root of the number. In Exercises 7 and 8, find the values of x and y that satisfy the equation. Algebra 2 53 Notetaking with Vocabulary (continued) In Exercises 9-14, simplify the expression. Then classify the result as a real number or imaginary number. If the res lt is n imaginary number, specify if it is a pure imaginary n be'I_ Algebra 2 15. Find the impedance of the series circuit. In Exercises 16-18, solve the equation. Check your solution(s). 16. 19. Sketch a graph of a function that has two real zeros at -2 and 2. Then sketch a graph on the same grid of a function that has two imaginary zeros of -2i and 2i. Explain the difference in the graphs of the two functions. 55