3.2/ 3.3 Complex Numbers and Complete the Square 24-25 H

Front

What is 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 imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as i = √(-1). It is used to represent the square root of negative numbers.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers (a + bi)(c + di), use the distributive property: ac + adi + bci + bdi². Remember that i² = -1.

Front

What is the result of (4-5i)(4+5i)?

Back

The result is 41.

Front

What does it mean to complete the square?

Back

Completing the square is a method used to convert a quadratic expression into a perfect square trinomial, making it easier to solve or analyze.

Front

How do you complete the square for the expression x² + 4x + 10?

Back

Rewrite it as (x + 2)² = -6.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots.