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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/Bookshelves/Applied_Mathematics/Math_in_Society_(Lippman)/15%3A_Fractals/15.04%3A_Complex_NumbersWhen we add −1+3i, we add -1 to the real part, moving the point 1 units to the left, and we add 5 to the imaginary part, moving the point 5 units vertically. \(\begin{array}{ll} (2+5 i)(4+i) & \t...When we add −1+3i, we add -1 to the real part, moving the point 1 units to the left, and we add 5 to the imaginary part, moving the point 5 units vertically. (2+5i)(4+i)Expand=8+20i+2i+5i2Since i=√−1,i2=−1=8+20i+2i+5(−1)Simplify=3+22i i⋅1+i⋅2i=i+2i2=i+2(−1)=−2+i (1+2i)(1+i)=1+i+2i+2i2=1+3i+2(−1)=−1+3i (−1+3i)(1+i)=−1−i+3i+3i2=−1+2i+3(−1)=−4+2i
- 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/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.
- https://math.libretexts.org/Courses/Hartnell_College/MATH_25%3A_PreCalculus_(Abramson_OpenStax)/03%3A_Polynomial_and_Rational_Functions/3.R%3A_Polynomial_and_Rational_Functions(Review)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/Hartnell_College/MATH_25%3A_PreCalculus_(Abramson_OpenStax)/03%3A_Polynomial_and_Rational_Functions/3.01%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/Coastline_College/Math_C170%3A_Precalculus_(Tran)/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/Coastline_College/Math_C170%3A_Precalculus_(Tran)/03%3A_Polynomial_and_Rational_Functions/3.R%3A_Polynomial_and_Rational_Functions(Review)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.R%3A_Polynomial_and_Rational_Functions(Review)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.
