Operations with Polynomials and Complex Numbers

Front

What is the standard form of a complex number?

Back

A complex number is written in the form a + bi, where a and b are real numbers, and i is the imaginary unit.

Front

How do you multiply two complex numbers (a + bi)(c + di)?

Back

Use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i.

Front

What is the result of (1 - 7i)^2?

Back

The result is -48 - 14i.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms.

Front

Back

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as (x - 4).

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms, such as (x^2 + 9x - 7).

Front

How do you multiply a binomial by a trinomial?

Back

Use the distributive property (FOIL) for each term in the binomial with each term in the trinomial.

Front

What is the result of multiplying (x - 4)(x^2 + 9x - 7)?

Back

Front

What is the imaginary unit 'i'?

Back