Solutions for Precalculus Enhanced with Graphing Utilities, Books a la Carte Edition Plus NEW MyLab Math -- Access Card Package (7th Edition)
Problem 1AYP:
The conjugate of 43i is _______. (p. A59)Problem 4AYP:
sin 120 = ; cos 240 = . (pp. 385-387)Problem 5CV:
In the complex plane, the x-axis is referred to as the _____ axis, and the y-axis is called the...Problem 6CV:
When a complex number z is written in the polar form z=r(cos+isin) , the nonnegative number r is the...Problem 7CV:
Let z 1 =r 1 (cos 1 +isin 1 ) and z 2 =r 2 (cos 2 +isin 2 ) be two complex numbers. Then z 1 z 2...Problem 11CV:
If z=x+yi is a complex number, then | z | equals which of the following? (a) x 2 + y 2 (b) | x |+| y...Problem 12CV:
If z 1 = r 1 ( cos 1 +isin 1 ) , and z 2 = r 2 ( cos 2 +isin 2 ) are complex numbers, then z 1 z...Problem 13SB:
In Problems 13-24, plot each complex number in the complex plane and write it in polar form. Express...Problem 17SB:
In Problems 13-24, plot each complex number in the complex plane and write it in polar form. Express...Problem 20SB:
In Problems 13-24, plot each complex number in the complex plane and write it in polar form. Express...Problem 21SB:
In Problems 13-24, plot each complex number in the complex plane and write it in polar form. Express...Problem 22SB:
In Problems 13-24, plot each complex number in the complex plane and write it in polar form. Express...Problem 23SB:
In Problems 13-24, plot each complex number in the complex plane and write it in polar form. Express...Problem 24SB:
In Problems 13-24, plot each complex number in the complex plane and write it in polar form. Express...Problem 25SB:
In Problems 25-34, write each complex number in rectangular form. 2( cos 120 +isin 120 )Problem 26SB:
In Problems 25-34, write each complex number in rectangular form. 3( cos 210 +isin 210 )Problem 27SB:
In Problems 25-34, write each complex number in rectangular form. 4( cos 7 4 +isin 7 4 )Problem 28SB:
In Problems 25-34, write each complex number in rectangular form. 2( cos 5 6 +isin 5 6 )Problem 29SB:
In Problems 25-34, write each complex number in rectangular form. 3( cos 3 2 +isin 3 2 )Problem 33SB:
In Problems 25-34, write each complex number in rectangular form. 2( cos 18 +isin 18 )Problem 34SB:
In Problems 25-34, write each complex number in rectangular form. 3( cos 10 +isin 10 )Problem 36SB:
In Problems 35-42, find zw and z w . Leave your answers in polar form. z=cos 120 +isin 120 w=cos...Problem 39SB:
In Problems 35-42, find zw and z w . Leave your answers in polar form. z=2( cos 8 +isin 8 ) w=2(...Problem 40SB:
In Problems 35-42, find zw and z w . Leave your answers in polar form. z=4( cos 3 8 +isin 3 8 ) w=2(...Problem 43SB:
In Problems 43-54, write each expression in the standard form . [ 4( cos 40 +isin 40 ) ] 3Problem 44SB:
In Problems 43-54, write each expression in the standard form a+bi . [ 3( cos 80 +isin 80 ) ] 3Problem 45SB:
In Problems 43-54, write each expression in the standard form a+bi . [ 2( cos 10 +isin 10 ) ] 5Problem 46SB:
In Problems 43-54, write each expression in the standard form a+bi . [ 2 ( cos 5 16 +isin 5 16 ) ] 4Problem 47SB:
In Problems 43-54, write each expression in the standard form a+bi . [ 3 ( cos 10 +isin 10 ) ] 6Problem 48SB:
In Problems 43-54, write each expression in the standard form a+bi . [ 1 2 ( cos 72 +isin 72 ) ] 5Problem 49SB:
In Problems 43-54, write each expression in the standard form a+bi . [ 5 ( cos 3 16 +isin 3 16 ) ] 4Problem 50SB:
In Problems 43-54, write each expression in the standard form a+bi . [ 3 ( cos 5 18 +isin 5 18 ) ] 6Problem 55SB:
In Problems 55-60, find all the complex roots. Leave your answers in polar form with the argument in...Problem 56SB:
In Problems 55-60, find all the complex roots. Leave your answers in polar form with the argument in...Problem 57SB:
In Problems 55-60, find all the complex roots. Leave your answers in polar form with the argument in...Problem 58SB:
In Problems 55-60, find all the complex roots. Leave your answers in polar form with the argument in...Problem 59SB:
In Problems 55-60, find all the complex roots. Leave your answers in polar form with the argument in...Problem 60SB:
In Problems 55-60, find all the complex roots. Leave your answers in polar form with the argument in...Problem 61SB:
Solve x 5 i=0 using the methods of this section.Problem 62SB:
Solve x 5 +i=0 using the methods of this section.Problem 65AE:
Show that each complex n th root of a nonzero complex number w has the same magnitude.Problem 66AE:
Use the result of Problem 65 to draw the conclusion that each complex n th root lies on a circle...Problem 67AE:
Refer to Problem 66. Show that the complex n th roots of a nonzero complex number w are equally...Problem 68AE:
Prove formula (6).Problem 69AE:
Prove that De Moivres Theorem is true for all integers n by assuming it is true for integers n1 and...Problem 70AE:
Mandelbrot Sets (a) Consider the expression a n = ( a n1 ) 2 +z , where z is some complex number...Problem 72RYK:
Problems 71-74 are based on material learned earlier in the course. The purpose of these problems is...Browse All Chapters of This Textbook
Chapter 1.1 - The Distance And Midpoint Formulas; Graphing Utilities; Introduction To Graphing EquationsChapter 1.2 - Intercepts; Symmetry; Graphing Key EquationsChapter 1.3 - Solving Equations Using A Graphing UtilityChapter 1.4 - LinesChapter 1.5 - CirclesChapter 1.R - ReviewChapter 2.1 - FunctionsChapter 2.2 - The Graph Of A FunctionChapter 2.3 - Properties Of FunctionsChapter 2.4 - Library Of Functions;piecewise-defined Functions
Chapter 2.5 - Graphing Techniques: TransformationsChapter 2.6 - Mathematical Models: Building FunctionsChapter 2.R - ReviewChapter 2.CR - Cumulative ReviewChapter 3.1 - Properties Of Linear Functions And Linear ModelsChapter 3.2 - Building Linear Models From DataChapter 3.3 - Quadratic Functions And Their PropertiesChapter 3.4 - Build Quadratic Models From Verbal Descriptions And From DataChapter 3.5 - Inequalities Involving Quadratic FunctionsChapter 3.R - Chapter ReviewChapter 3.CT - Chapter TestChapter 3.CR - Cumulative ReviewChapter 4.1 - Polynomial Functions And ModelsChapter 4.2 - The Real Zeros Of A Polynomial FunctionChapter 4.3 - Complex Zeros; Fundamental Theorem Of AlgebraChapter 4.4 - Properties Of Rational FunctionsChapter 4.5 - The Graph Of A Rational FunctionChapter 4.6 - Polynomial And Rational InequalitiesChapter 5.1 - Composite FunctionsChapter 5.2 - One-to-one Functions; Inverse FunctionsChapter 5.3 - Exponential FunctionsChapter 5.4 - Logarithmic FunctionsChapter 5.5 - Properties Of LogarithmsChapter 5.6 - Logarithmic And Exponential EquationsChapter 5.7 - Financial ModelsChapter 5.8 - Exponential Growth And Decay Models; Newton’s Law; Logistic Growth And Decay ModelsChapter 5.9 - Building Exponential, Logarithmic, And Logistic Models From DataChapter 5.R - ReviewChapter 6.1 - Angles And Their MeasureChapter 6.2 - Trigonometric Functions: Unit Circle ApproachChapter 6.3 - Properties Of The Trigonometric FunctionsChapter 6.4 - Graphs Of The Sine And Cosine FunctionsChapter 6.5 - Graphs Of The Tangent, Cotangent, Cosecant, And Secant FunctionsChapter 6.6 - Phase Shift; Sinusoidal Curve FittingChapter 7.1 - The Inverse Sine, Cosine, And Tangent FunctionsChapter 7.2 - The Inverse Trigonometric Functions (continued)Chapter 7.3 - Trigonometric EquationsChapter 7.4 - Trigonometric IdentitiesChapter 7.5 - Sum And Difference FormulasChapter 7.6 - Double-angle And Half-angle FormulasChapter 7.7 - Product-to-sum And Sum-to-product FormulasChapter 7.R - ReviewChapter 8.1 - Right Triangle Trigonometry; ApplicationsChapter 8.2 - The Law Of SinesChapter 8.3 - The Law Of CosinesChapter 8.4 - Area Of A TriangleChapter 8.5 - Simple Harmonic Motion; Damped Motion; Combining WavesChapter 8.R - ReviewChapter 9.1 - Polar CoordinatesChapter 9.2 - Polar Equations And GraphsChapter 9.3 - The Complex Plane; De Moivre’s TheoremChapter 9.4 - VectorsChapter 9.5 - The Dot ProductChapter 9.6 - Vectors In SpaceChapter 9.7 - The Cross ProductChapter 10.2 - The ParabolaChapter 10.3 - The EllipseChapter 10.4 - The HyperbolaChapter 10.5 - Rotation Of Axes; General Form Of A ConicChapter 10.6 - Polar Equations Of ConicsChapter 10.7 - Plane Curves And Parametric EquationsChapter 10.R - ReviewChapter 11.1 - Systems Of Linear Equations: Substitution And EliminationChapter 11.2 - Systems Of Linear Equations: MatricesChapter 11.3 - Systems Of Linear Equations: DeterminantsChapter 11.4 - Matrix AlgebraChapter 11.5 - Partial Fraction DecompositionChapter 11.6 - Systems Of Nonlinear EquationsChapter 11.7 - Systems Of InequalitiesChapter 11.8 - Linear ProgrammingChapter 12.1 - SequencesChapter 12.2 - Arithmetic SequencesChapter 12.3 - Geometric Sequences; Geometric SeriesChapter 12.4 - Mathematical InductionChapter 12.5 - The Binomial TheoremChapter 13.1 - CountingChapter 13.2 - Permutations And CombinationsChapter 13.3 - ProbabilityChapter 13.R - ReviewChapter 14.1 - Finding Limits Using Tables And GraphsChapter 14.2 - Algebra Techniques For Finding LimitsChapter 14.3 - One-sided Limits; Continuous FunctionsChapter 14.4 - The Tangent Problem; The DerivativeChapter 14.5 - The Area Problem; The IntegralChapter A.1 - Algebra EssentialsChapter A.2 - Geometry EssentialsChapter A.3 - PolynomialsChapter A.4 - Synthetic DivisionChapter A.5 - Rational ExpressionsChapter A.6 - Solving EquationsChapter A.7 - Complex Numbers; Quadratic Equations In The Complex Number SystemChapter A.8 - Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job ApplicationsChapter A.9 - Interval Notation; Solving InequalitiesChapter A.10 - Nth Roots; Rational ExponentsChapter B - The Limit Of A Sequence; Infinite Series
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