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- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/03%3A_Polynomial_and_Rational_Functions/3.E%3A_Polynomial_and_Rational_Functions(Exercises)After all, to this point we have described the square root of a negative number as undefined. Fortunately, there is another system of numbers that provides solutions to problems such as these. In this...After all, to this point we have described the square root of a negative number as undefined. Fortunately, there is another system of numbers that provides solutions to problems such as these. In this section, we will explore this number system and how to work within it.
- https://math.libretexts.org/Courses/Highline_College/Math_141%3A_Precalculus_I_(old_edition)/03%3A_Polynomial_and_Rational_Functions/3.01%3A_Complex_Numbers_ReviewAfter all, to this point we have described the square root of a negative number as undefined. Fortunately, there is another system of numbers that provides solutions to problems such as these. In this...After all, to this point we have described the square root of a negative number as undefined. Fortunately, there is another system of numbers that provides solutions to problems such as these. In this section, we will explore this number system and how to work within it.
- https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/02%3A_Algebra_Support/2.23%3A_Complex_Numbers\(\begin{array}{cccc}{i^{5}} \qquad& {i^{6}} \qquad& {i^{7}} \qquad& {i^{8}} \\ {i^{4} \cdot i} \qquad& {i^{4} \cdot i^{2}} \qquad& {i^{4} \cdot i^{3}} \qquad& {i^{4} \cdot i^{4}} \\ {1 \cdot i} \qqua...\(\begin{array}{cccc}{i^{5}} \qquad& {i^{6}} \qquad& {i^{7}} \qquad& {i^{8}} \\ {i^{4} \cdot i} \qquad& {i^{4} \cdot i^{2}} \qquad& {i^{4} \cdot i^{3}} \qquad& {i^{4} \cdot i^{4}} \\ {1 \cdot i} \qquad& {1 \cdot i^{2}} \qquad& {1 \cdot i^{3}} \qquad& {1 \cdot 1} \\ {i} \qquad& {i^{2}} & {i^{3}} \qquad& {1} \\ {}&\qquad&{-1} & {-i}\end{array}\)
- https://math.libretexts.org/Courses/Angelo_State_University/Finite_Mathematics/02%3A_Equations_and_Inequalities/2.04%3A_Complex_NumbersIn this section, we will explore a set of numbers that fills voids in the set of real numbers and find out how to work within it.
- https://math.libretexts.org/Courses/Chabot_College/Chabot_College_College_Algebra_for_BSTEM/02%3A_Equations_and_Inequalities/2.04%3A_Complex_NumbersThe square root of any negative number can be written as a multiple of i. To plot a complex number, we use two number lines, crossed to form the complex plane. The horizontal axis is the real axis, an...The square root of any negative number can be written as a multiple of i. To plot a complex number, we use two number lines, crossed to form the complex plane. The horizontal axis is the real axis, and the vertical axis is the imaginary axis. Complex numbers can be added and subtracted by combining the real parts and combining the imaginary parts. Complex numbers can be multiplied and divided.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_2e_(OpenStax)/08%3A_Further_Applications_of_Trigonometry/8.06%3A_Polar_Form_of_Complex_NumbersIn this section, we will focus on the mechanics of working with complex numbers: translation of complex numbers from polar form to rectangular form and vice versa, interpretation of complex numbers in...In this section, we will focus on the mechanics of working with complex numbers: translation of complex numbers from polar form to rectangular form and vice versa, interpretation of complex numbers in the scheme of applications, and application of De Moivre’s Theorem.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_2e_(OpenStax)/03%3A_Polynomial_and_Rational_Functions/3.02%3A_Complex_NumbersAfter all, to this point we have described the square root of a negative number as undefined. Fortunately, there is another system of numbers that provides solutions to problems such as these. In this...After all, to this point we have described the square root of a negative number as undefined. Fortunately, there is another system of numbers that provides solutions to problems such as these. In this section, we will explore this number system and how to work within it.
- https://math.libretexts.org/Courses/Truckee_Meadows_Community_College/TMCC%3A_Precalculus_I_and_II/Under_Construction_test2_08%3A_Further_Applications_of_Trigonometry/Under_Construction_test2_08%3A_Further_Applications_of_Trigonometry_8.5%3A_Polar_Form_of_Complex_NumbersIn this section, we will focus on the mechanics of working with complex numbers: translation of complex numbers from polar form to rectangular form and vice versa, interpretation of complex numbers in...In this section, we will focus on the mechanics of working with complex numbers: translation of complex numbers from polar form to rectangular form and vice versa, interpretation of complex numbers in the scheme of applications, and application of De Moivre’s Theorem.
- https://math.libretexts.org/Bookshelves/Algebra/College_Algebra_1e_(OpenStax)/02%3A_Equations_and_Inequalities/2.05%3A_Complex_NumbersThe square root of any negative number can be written as a multiple of i. To plot a complex number, we use two number lines, crossed to form the complex plane. The horizontal axis is the real axis, an...The square root of any negative number can be written as a multiple of i. To plot a complex number, we use two number lines, crossed to form the complex plane. The horizontal axis is the real axis, and the vertical axis is the imaginary axis. Complex numbers can be added and subtracted by combining the real parts and combining the imaginary parts. Complex numbers can be multiplied and divided.
- https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/04%3A_Polynomial_and_Rational_Functions/4.E%3A_Polynomial_and_Rational_Functions_(Exercises)For the exercises 75-78, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function. The \(x\)-intercept is where the graph of...For the exercises 75-78, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function. The \(x\)-intercept is where the graph of the function crosses the \(x\)-axis, and the zero of the function is the input value for which \(f(x)=0\).
- https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.04%3A_Polynomial_and_Rational_Functions/1.4.E%3A_Polynomial_and_Rational_Functions_(Exercises)For the exercises 75-78, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function. The \(x\)-intercept is where the graph of...For the exercises 75-78, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function. The \(x\)-intercept is where the graph of the function crosses the \(x\)-axis, and the zero of the function is the input value for which \(f(x)=0\).
