Flashcard +, -, X Complex Numbers & Powers of i

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.

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CCSS.HSN.CN.A.1

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as i = √(-1). It is used to extend the real number system to include solutions to equations that do not have real solutions.

Tags

CCSS.HSN.CN.A.1

Front

How do you add complex numbers?

Back

To add complex numbers, combine their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Tags

CCSS.HSN.CN.A.2

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

Tags

CCSS.HSN.CN.A.2

Front

What is the product of two complex numbers?

Back

The product of two complex numbers (a + bi) and (c + di) is given by (ac - bd) + (ad + bc)i.

Tags

CCSS.HSN.CN.A.2

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used to simplify the division of complex numbers.

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CCSS.HSN.CN.A.3

Front

How do you divide complex numbers?

Back

To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator. For example, (a + bi) / (c + di) = [(a + bi)(c - di)] / (c^2 + d^2).

Tags

CCSS.HSN.CN.A.3

Front

What is the power of 'i'?

Back

The powers of 'i' cycle every four: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1. For any integer n, i^n can be determined by n mod 4.

Tags

CCSS.HSN.CN.A.2

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = ax^n + bx^(n-1) + ... + k.

Front

What does it mean to factor a polynomial?

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Factoring a polynomial means expressing it as a product of simpler polynomials or factors. For example, x^2 - 5x + 6 can be factored as (x - 2)(x - 3).