Chapter 3 Complex Numbers Quadratic Functions and Equations Inequalities Rational Equations Radical Equations Absolute Value Equations
Willa Cather –U.S. novelist Art, it seems to me, should simplify. That indeed, is very nearly the whole of the higher artistic process; finding what conventions of form and what detail one can do without and yet preserve the spirit of the whole – so that all one has suppressed and cut away is there to the readers consciousness as much as if it were in type on the page.
Add and subtract complex #s Add or subtract the real and imaginary parts of the numbers separately.
Orison Swett Marden All who have accomplished great things have had a great aim, have fixed their gaze on a goal which was high, one which sometimes seemed impossible.
Multiply Complex #s Multiply as if two polynomials and combine like terms as in the FOIL Note i squared = -1
Complex Conjugates a – bi is the conjugate of a + bi The product is a rational number
Divide Complex #s Multiply numerator and denominator by complex conjugate of denominator. Write answer in standard form
Harry Truman – American President A pessimist is one who makes difficulties of his opportunities and an optimist is one who makes opportunities of his difficulties.
Calculator and Complex #s Use Mode – Complex Use i second function of decimal point Use [Math] [Frac] and place in standard form a + bi Can add, subtract, multiply, and divide complex numbers with calculator.
Mathematics 116 Solving Quadratic Equations Algebraically This section contains much information
Def: Quadratic Function General Form a,b,c,are real numbers and a not equal 0
Objective – Solve quadratic equations Two distinct solutions One Solution – double root Two complex solutions Solve for exact and decimal approximations
Solving Quadratic Equation #1 Factoring Use zero Factor Theorem Set = to 0 and factor Set each factor equal to zero Solve Check
Solving Quadratic Equation #2 Graphing Solve for y Graph and look for x intercepts Can not give exact answers Can not do complex roots.
Solving Quadratic Equations #3 Square Root Property For any real number c
Dorothy Broude Act as if it were impossible to fail.
Completing the square informal Make one side of the equation a perfect square and the other side a constant. Then solve by methods previously used.
Procedure: Completing the Square 1. If necessary, divide so leading coefficient of squared variable is 1. 2. Write equation in form 3. Complete the square by adding the square of half of the linear coefficient to both sides. 4. Use square root property 5. Simplify