Completing the Square, Imaginary and Complex Numbers

Flashcards on completing the square method, imaginary numbers, and complex numbers.

Perfect Squares

Polynomials on the left-hand side that can be factored into the form of (x ± k)^2.

Subtract c from both sides

Move the constant term to the other side of the equation.

Divide both sides by a

Divide all terms by the coefficient of the squared term.

Add the square of half the coefficient of x to both sides

Add the square of half the coefficient of x to both sides of the equation, (b/2)^2.

Write the left side as a perfect square

Rewrite the side with the variables as a perfect square.

Solve the obtained equation Using method number two

Solve the equation by taking the square root of both sides.

Imaginary Number

A number that when squared gives a negative result; i^2 = -1

Square root of negative a

√(-a) = √a * i

Complex Number

A number that can be expressed in the form a + bi, where a and b are real numbers.

Real Part

The real number 'a' in a complex number a + bi.

Imaginary Part

The real number 'b' in a complex number a + bi.

Conjugate

A complex number with the same real part but the opposite imaginary part.

Multiply both numerator and denominator

Multiply both the numerator and denominator by the conjugate of the denominator.