4.1.7 Flashcard Review (Review A)

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you solve a quadratic equation using the quadratic formula?

Back

To solve a quadratic equation ax^2 + bx + c = 0 using the quadratic formula, use x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates 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.

Front

What is the process for simplifying complex numbers?

Back

To simplify complex numbers, combine like terms (real parts with real parts and imaginary parts with imaginary parts) and express the result in the form a + bi.

Front

How do you add two complex numbers?

Back

To add two complex numbers, (a + bi) + (c + di), combine the real parts (a + c) and the imaginary parts (b + d) to get (a + c) + (b + d)i.

Front

What is the product of two complex numbers in the form (a + bi)(c + di)?

Back

The product is given by (ac - bd) + (ad + bc)i.

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, (a + bi) - (c + di), subtract the real parts (a - c) and the imaginary parts (b - d) to get (a - c) + (b - d)i.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi.

Front

How do you multiply a complex number by its conjugate?

Back

Multiplying a complex number a + bi by its conjugate a - bi results in a² + b², which is a real number.

Front

What is the significance of the imaginary unit i?

Back

The imaginary unit i is defined as √(-1), and it is used to express complex numbers.