MathsComplex Numbers and Quadratic Equations: Definition and Exercises

Complex Numbers and Quadratic Equations: Definition and Exercises

Complex Numbers and Quadratic Equations

Complex numbers are a mathematical structure that allows us to work with numbers that are not real. A complex number is written as a + bi, where a is the real part and b is the imaginary part. The real part is the part that is like a regular number, and an imaginary part is a number multiplied by I, equal to the square root of -1. Complex numbers can be used to solve quadratic equations.

Complex Quadratic Equations

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    Complex numbers can be expressed as a + bi, where a and b are real numbers, and i is the imaginary unit. The square root of a negative number is imaginary. Quadratic equations are equations in the form ax2 + bx + c = 0, where a, b, and c are real numbers.

    Complex numbers can be used to solve quadratic equations. For example, the quadratic equation x2 + 4x – 3 = 0 can be solved using the complex number 3 + 2i. First, factor the equation x2 + 4x – 3 = 0 into (x + 3)2 = 0. Next, take the square root of each side of the equation.

    x + 3 = 0
    x = -3

    The complex number 3 + 2i can be used to solve the equation x2 + 4x – 3 = 0. First, multiply 3 + 2i by itself.

    3 + 2i = (3)(3) + (2)(2)i

    Next, take the square root of each side of the equation.

    3 + 2i = 9 + 4i

    The complex number 3 + 2i is a solution to the equation x2 + 4x – 3 = 0.

    Complex numbers are a set of numbers that are used in mathematics and physics. They are created by taking a real number and adding an imaginary number. This imaginary number is created by taking the square root of -1. This number is written as i. Complex numbers can be graphed on a coordinate plane. The real number is graphed on the x-axis, and the imaginary number is graphed on the y-axis.

    Quadratic equations are equations that have a squared variable. This variable is usually x. Quadratic equations can be solved by using the quadratic formula. This formula is written as:

    The solutions to the equation are the values of x that make the equation true.

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