Algebra II Quadratics and Imaginary Numbers

A quadratic equation is a polynomial equation of degree 2, typically in the form $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and a ≠ 0.

The quadratic formula is used to find the solutions of a quadratic equation and is given by $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ .

The discriminant, given by $$D = b^2 - 4ac$$ , determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are two complex roots.

The simplified form is $$22 - 6i$$ .

The result is $$60 - 32i$$ .

Imaginary numbers are numbers that can be written as a real number multiplied by the imaginary unit $$i$$ , where $$i = \sqrt{-1}$$ .

The standard form of a complex number is $$a + bi$$ , where a is the real part and b is the imaginary part.

The imaginary part of a complex number $$a + bi$$ is the coefficient b of $$i$$ .

The real part of a complex number $$a + bi$$ is the coefficient a.

To add two complex numbers, add their real parts and their imaginary parts separately: $$(a + bi) + (c + di) = (a + c) + (b + d)i$$ .