Exam Review - Simplifying Square Roots and Systems of Equations

Front

Define a complex number.

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Front

What is the process of simplifying a complex number?

Back

To simplify a complex number, combine like terms by adding or subtracting the real parts and the imaginary parts separately.

Front

Simplify: (-10 + 4i) - (15 - 14i)

Back

-25 + 18i

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 simultaneously.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

Find ALL solutions to the system of non-linear equations: 5x^2 - 2y^2 = 27 and 4x^2 - y^2 = 51.

Back

(5, ±7) & (-5, ±7)

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any square roots or irrational numbers from the denominator of a fraction.

Front

Rationalize the denominator: \( \frac{\sqrt{3}}{\sqrt{15}} \)

Back

\( \frac{\sqrt{5}}{5} \)

Front

What is a non-linear equation?

Back

A non-linear equation is an equation in which the variables are raised to a power greater than one or multiplied together, resulting in a graph that is not a straight line.

Front

Find ALL solutions to the system of non-linear equations: x^2 + 3y^2 = 28 and x^2 - y^2 = 12.

Back

(4, ±2) & (-4, ±2)