Chapter 3 Test

Front

What is the standard form of a complex number?

Back

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

Front

How do you add two complex numbers?

Back

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

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations in the system.

Front

How do you solve a system of equations using substitution?

Back

To solve a system using substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax^2 + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean to set an equation equal to zero?

Back

Setting an equation equal to zero is a common step in solving equations, particularly quadratic equations, to find the values of the variable that make the equation true.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is less than, greater than, less than or equal to, or greater than or equal to the other.

Front

How do you solve a quadratic inequality?

Back

To solve a quadratic inequality, first solve the corresponding quadratic equation, then test intervals to determine where the inequality holds true.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, two complex roots.

Front

What is the process for solving quadratic equations by factoring?

Back

To solve by factoring, rewrite the quadratic equation in the form (x - p)(x - q) = 0, then set each factor equal to zero to find the solutions x = p and x = q.