Solutions for Precalculus
Problem 1SP:
Write each expression in terms of i . a.81b.50c.11Problem 2SP:
Simplify. a.i13b.i103c.i64d.i30Problem 4SP:
Multiply. Write the result in the form a+bi . 5+4i3iProblem 11SP:
Solve. 2t2/3=157t1/3Problem 1PE:
The imaginary number i is defined so that i=1andi2=.Problem 2PE:
For a positive real number b, the value b=.Problem 3PE:
Given a complex number a+bi , the value of a is called the part and the value of b is called the ...Problem 5PE:
The equation m2/3+10m1/3+9=0 is said to be in form, because making the substitution u= results in a...Problem 6PE:
Consider the equation 4x2+12+44x2+1+4=0. if the substitution u= is made, then the equation becomes...Problem 7PE:
For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 121Problem 8PE:
For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 100Problem 9PE:
For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 98Problem 11PE:
For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 49Problem 12PE:
For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 136Problem 13PE:
For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 105Problem 14PE:
For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 615Problem 15PE:
For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 982Problem 16PE:
For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 455Problem 17PE:
For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 637Problem 19PE:
For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 8+3i14Problem 20PE:
For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 4+5i6Problem 21PE:
For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 46i2Problem 22PE:
For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 915i3Problem 23PE:
For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 18+484Problem 24PE:
For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 20+5010Problem 25PE:
For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 14987Problem 26PE:
For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 10+1255Problem 31PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 33PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 34PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 35PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 37PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 39PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 40PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 41PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 42PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 43PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 45PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 47PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 48PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 49PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 50PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 51PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 53PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 54PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 55PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 56PE:
For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi....Problem 73PE:
For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of...Problem 74PE:
For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of...Problem 75PE:
For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of...Problem 76PE:
For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of...Problem 77PE:
For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of...Problem 78PE:
For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of...Problem 79PE:
For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of...Problem 80PE:
For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of...Problem 81PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 82PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 83PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 84PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 85PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 86PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 87PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 88PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 89PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 90PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 91PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 92PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 93PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 94PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 95PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 96PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 97PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 98PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 99PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 100PE:
For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11)...Problem 101PE:
For Exercises 101-104, verify by substitution that the given values of x are solutions to the given...Problem 102PE:
For Exercises 101-104, verify by substitution that the given values of x are solutions to the given...Problem 103PE:
For Exercises 101-104, verify by substitution that the given values of x are solutions to the given...Problem 104PE:
For Exercises 101-104, verify by substitution that the given values of x are solutions to the given...Problem 105PE:
Prove thata+bic+di=acbd+ad+bci.Problem 106PE:
Prove that a+bi2=a2b2+2abi.Problem 107PE:
For Exercises 107-108, solve the equation in two ways. a. Solve as a radical equation by first...Problem 108PE:
For Exercises 107-108, solve the equation in two ways. a. Solve as a radical equation by first...Problem 109PE:
Explain the flaw in the following logic. 94=94=36=6Problem 110PE:
Discuss the difference between the products a+babanda+biabi.Problem 112PE:
Give an example of two complex numbers that are not real numbers, but whose product is a real...Problem 113PE:
Given a quadratic equation, what is the discriminant and what information does it provide about the...Problem 115PE:
For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance,...Problem 116PE:
For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance,...Problem 117PE:
For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance,...Problem 118PE:
For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance,...Problem 119PE:
For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance,...Problem 120PE:
For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance,...Problem 121PE:
For Exercise 121-124, write an equation with integer coefficients and the variable x that has the...Problem 122PE:
For Exercise 121-124, write an equation with integer coefficients and the variable x that has the...Browse All Chapters of This Textbook
Chapter R - Review Of PrerequisitesChapter R.1 - Sets And The Real Number LineChapter R.2 - Exponents And RadicalsChapter R.3 - Polynomials And FactoringChapter R.4 - Rational Expressions And More Operations On RadicalsChapter R.5 - Equations With Real SolutionsChapter R.6 - Complex Numbers And More Quadratic EquationsChapter R.7 - Applications Of EquationsChapter R.8 - Linear, Compound, And Absolute Value InequalitiesChapter 1 - Functions And Relations
Chapter 1.1 - The Rectangular Coordinate System And Graphing UtilitiesChapter 1.2 - CirclesChapter 1.3 - Functions And RelationsChapter 1.4 - Linear Equations In Two Variables And Linear FunctionsChapter 1.5 - Applications Of Linear Equations And ModelingChapter 1.6 - Transformations Of GraphsChapter 1.7 - Analyzing Graphs Of Functions And Piecewise-defined FunctionsChapter 1.8 - Algebra Of Functions And Function CompositionChapter 2 - Polynomial And Rational FunctionsChapter 2.1 - Quadratic Functions And ApplicationsChapter 2.2 - Introduction To Polynomial FunctionsChapter 2.3 - Division Of Polynomials And The Remainder And Factor TheoremsChapter 2.4 - Zeros Of PolynomialsChapter 2.5 - Rational FunctionsChapter 2.6 - Polynomial And Rational InequalitiesChapter 2.7 - VariationChapter 3 - Exponential And Logarithmic FunctionsChapter 3.1 - Inverse FunctionsChapter 3.2 - Exponential FunctionsChapter 3.3 - Logarithmic FunctionsChapter 3.4 - Properties Of LogarithmsChapter 3.5 - Exponential And Logarithmic Equations And ApplicationsChapter 3.6 - Modeling With Exponential And Logarithmic FunctionsChapter 4 - Trigonometric FunctionsChapter 4.1 - Angles And Their MeasureChapter 4.2 - Trigonometric Functions Defined On The Unit CircleChapter 4.3 - Right Triangle TrigonometryChapter 4.4 - Trigonometric Functions Of Any AngleChapter 4.5 - Graphs Of Sine And Cosine FunctionsChapter 4.6 - Graphs Of Other Trigonometric FunctionsChapter 4.7 - Inverse Trigonometric FunctionsChapter 5 - Analytic TrigonometryChapter 5.1 - Fundamental Trigonometric IdentitiesChapter 5.2 - Sum And Difference FormulasChapter 5.3 - Double-angle, Power-reducing, And Half-angle FormulasChapter 5.4 - Product-to-sum And Sum-to-product FormulasChapter 5.5 - Trigonometric EquationsChapter 6 - Applications Of Trigonometric FunctionsChapter 6.1 - Applications Of Right TrianglesChapter 6.2 - The Law Of SinesChapter 6.3 - The Law Of CosinesChapter 6.4 - Harmonic MotionChapter 7 - Trigonometry Applied To Polar Coordinate Systems And VectorsChapter 7.1 - Polar CoordinatesChapter 7.2 - Graphs Of Polar EquationsChapter 7.3 - Complex Numbers In Polar FormChapter 7.4 - VectorsChapter 7.5 - Dot ProductChapter 8 - Systems Of Equations And InequalitiesChapter 8.1 - Systems Of Linear Equations In Two Variables And ApplicationsChapter 8.2 - Systems Of Linear Equations In Three Variables And ApplicationsChapter 8.3 - Partial Fraction DecompositionChapter 8.4 - Systems Of Nonlinear Equations In Two VariablesChapter 8.5 - Inequalities And Systems Of Inequalities In Two VariablesChapter 8.6 - Linear ProgrammingChapter 9 - Matrices And Determinants And ApplicationsChapter 9.1 - Solving Systems Of Linear Equations Using MatricesChapter 9.2 - Inconsistent Systems And Dependent EquationsChapter 9.3 - Operations On MatricesChapter 9.4 - Inverse Matrices And Matrix EquationsChapter 9.5 - Determinants And Cramer’s RuleChapter 10 - Analytic GeometryChapter 10.1 - The EllipseChapter 10.2 - The HyperbolaChapter 10.3 - The ParabolaChapter 10.4 - Rotation Of AxesChapter 10.5 - Polar Equations Of ConicsChapter 10.6 - Plane Curves And Parametric EquationsChapter 11 - Sequences, Series, Induction, And ProbabilityChapter 11.1 - Sequences And SeriesChapter 11.2 - Arithmetic Sequences And SeriesChapter 11.3 - Geometric Sequences And SeriesChapter 11.4 - Mathematical InductionChapter 11.5 - The Binomial TheoremChapter 11.6 - Principles Of CountingChapter 11.7 - Introduction To Probability
Book Details
Julie Miller wrote her developmental math series because students were coming into her Precalculus course underprepared. They weren’t mathematically mature enough to understand the concepts of math nor were they fully engaged with the material. She began her developmental mathematics offerings with intermediate algebra to help bridge that gap. The Precalculus series is a carefully constructed end to that bridge that uses the highly effective pedagogical features from her fastest growing developmental math series. What sets Julie Miller’s series apart is that it addresses course issues through an author-created digital package that maintains a consistent voice and notation throughout the program. This consistency--in videos, PowerPoints, Lecture Notes, and Group Activities--coupled with the power of ALEKS and Connect Hosted by ALEKS, ensures that students master the skills necessary to be successful in Precalculus and can carry them through to the calculus sequence.
Sample Solutions for this Textbook
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