How do you simplify $$i^{n}$$ for any integer n?

To simplify $$i^{n}$$ , use the fact that $$i^1 = i$$ , $$i^2 = -1$$ , $$i^3 = -i$$ , and $$i^4 = 1$$ . The powers of $$i$$ repeat every four terms.

What is the value of $$i^{216}$$ ?

$$i^{216} = 1$$ , since 216 mod 4 = 0.

What is the value of $$i^{451}$$ ?

$$i^{451} = -i$$ , since 451 mod 4 = 3.

What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root, given by $$b^2 - 4ac$$ . It determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, two complex roots.

What is the standard form of a quadratic equation?

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

What is the vertex form of a quadratic function?

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

What is the significance of the imaginary unit $$i$$ ?

The imaginary unit $$i$$ allows for the extension of the real number system to include solutions to equations that do not have real solutions, such as $$x^2 + 1 = 0$$ .

How do you multiply complex numbers?

To multiply complex numbers, use the distributive property. For example, (3 + 2i)(4 - 5i) = 12 - 15i + 8i - 10i^2 = 12 - 7i + 10 = 22 - 7i.

What is the conjugate of a complex number?

The conjugate of a complex number $$a + bi$$ is $$a - bi$$ . It is used in division to eliminate the imaginary part from the denominator.

What is the relationship between the roots and coefficients of a quadratic equation?

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

What is the importance of the quadratic formula?

The quadratic formula provides a method to find the roots of any quadratic equation, allowing for the solution of problems in various fields such as physics, engineering, and economics.

Adv Quadratic Formula and Complex Numbers Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

2.

FLASHCARD QUESTION

Front

What are complex numbers?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately. For example, for (3 + 2i) + (4 - 5i), the result is (3 + 4) + (2i - 5i) = 7 - 3i.

7.

FLASHCARD QUESTION

Front

What is the square root of a negative number?

Back

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