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Exam 8: Complex Numbers and Polar Coordinates

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Exam 1: The Six Trigonometric Functions158 Questionsadd course
Exam 2: Right Triangle Trigonometry181 Questionsadd course
Exam 3: Radian Measure157 Questionsadd course
Exam 4: Graphing and Inverse Functions156 Questionsadd course
Exam 5: Identities and Formulas186 Questionsadd course
Exam 6: Equations134 Questionsadd course
Exam 7: Triangles225 Questionsadd course
Exam 8: Complex Numbers and Polar Coordinates177 Questionsadd course
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Write the equation in polar coordinates. Write the equation in polar coordinates.

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Question 101

Read the method of solving the system of equations. ​ Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​ ​ Solving the first equation for  y , we have  Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​ . Substituting this value of  y  into the second equation, we have ​ Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​ ​ Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​ ​ Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​ Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​   Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​   Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​   Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​   ​ Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​ ​ Use the method shown above to solve the system of equations. Read the method of solving the system of equations. ​ ​ Solving the first equation for  y , we have  . Substituting this value of  y  into the second equation, we have ​ ​ The equation is quadratic. We write it in standard form and apply the quadratic formula. ​ ​         ​ ​ Use the method shown above to solve the system of equations. ​ ​

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Question 102

Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. ​ ​

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Question 103

Solve the equation. Leave your solution in trigonometric form. Solve the equation. Leave your solution in trigonometric form.

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Question 104

Solve the equation. Leave your solution in trigonometric form. Solve the equation. Leave your solution in trigonometric form.

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Question 105

Write the complex number in standard form. Write the complex number in standard form. ​ ​

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Question 106

Write the expression Write the expression  in terms of i and then simplify. ​  in terms of i and then simplify. ​

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Question 107

Find the product. Find the product. ​ ​

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Question 108

Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.

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Question 109

Graph the complex number and give the absolute value of the number. Graph the complex number and give the absolute value of the number. ​ ​

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Question 110

Convert to rectangular coordinates. Use exact values. Convert to rectangular coordinates. Use exact values. ​ ​

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Question 111

Find three cube roots for the complex number. Leave your answers in trigonometric form. Find three cube roots for the complex number. Leave your answers in trigonometric form.

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Question 112

Combine the complex numbers. Combine the complex numbers.

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Question 113

Sketch the graph of the equation by making a table using values of θ  that are multiples of 45°. Sketch the graph of the equation by making a table using values of θ  that are multiples of 45°. ​ ​

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Question 114

Find two square roots for the complex number. Write your answer in standard form. Find two square roots for the complex number. Write your answer in standard form.

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Question 115

Find 4 fourth roots of Find 4 fourth roots of . Write each root in standard form. . Write each root in standard form.

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Question 116

Graph the complex number and give the absolute value of it. Graph the complex number and give the absolute value of it. ​ ​

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Question 117

Graph the complex number along with its opposite and conjugate. Graph the complex number along with its opposite and conjugate. ​ ​

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Question 118

Find three cube roots for the complex number. Leave your answers in trigonometric form. Find three cube roots for the complex number. Leave your answers in trigonometric form.

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Question 119

Graph the equation. Graph the equation. ​ ​

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Question 120
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