Imaginary Number Intro

Front

What is an imaginary number?

Back

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is an expression written in descending order of the powers of the variable, typically represented as a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0.

Front

How do you combine like terms in a polynomial?

Back

To combine like terms in a polynomial, you add or subtract the coefficients of terms that have the same variable raised to the same power.

Front

What is the process for simplifying an expression involving imaginary numbers?

Back

To simplify an expression involving imaginary numbers, combine like terms and apply the property that i^2 = -1 to reduce powers of i.

Front

What does it mean to solve an equation using square roots?

Back

Solving an equation using square roots involves isolating the variable and then taking the square root of both sides of the equation, considering both the positive and negative roots.

Front

What is the result of the square root of a negative number?

Back

The square root of a negative number results in an imaginary number, expressed as a real number multiplied by 'i'.

Front

How do you write a polynomial in standard form?

Back

To write a polynomial in standard form, rearrange the terms so that the powers of the variable are in descending order, from highest to lowest.

Front

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

Back

The imaginary unit 'i' is significant because it 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.

Front

What is the simplified form of 10i?

Back

The simplified form of 10i is simply 10i, as it is already in its simplest form.

Front

What is the result of adding two imaginary numbers, such as 3i and 4i?

Back

The result of adding two imaginary numbers like 3i and 4i is 7i, by combining the coefficients.