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6.12: Finding Imaginary Solutions

Difficulty Level: At Grade Created by: CK-12
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Practice Fundamental Theorem of Algebra
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Vocabulary

Complex Conjugate

Complex conjugates are pairs of complex binomials. The complex conjugate of a+bi is a-bi. When complex conjugates are multiplied, the result is a single real number.

complex number

A complex number is the sum of a real number and an imaginary number, written in the form a + bi.

conjugate pairs theorem

The conjugate pairs theorem states that if f(z) is a polynomial of degree n, with n\ne0 and with real coefficients, and if f(z_{0})=0, where z_{0}=a+bi, then f(z_{0}^{*})=0. Where z_{0}^{*} is the complex conjugate of z_{0}.

fundamental theorem of algebra

The fundamental theorem of algebra states that if f(x) is a polynomial of degree n\ge 1, then f(x) has at least one zero in the complex number domain. In other words, there is at least one complex number c such that f(c)=0. The theorem can also be stated as follows: an n^{th} degree polynomial with real or complex coefficients has, with multiplicity, exactly n complex roots.

Imaginary Number

An imaginary number is a number that can be written as the product of a real number and i.

Imaginary Numbers

An imaginary number is a number that can be written as the product of a real number and i.

Polynomial

A polynomial is an expression with at least one algebraic term, but which does not indicate division by a variable or contain variables with fractional exponents.

Roots

The roots of a function are the values of x that make y equal to zero.

Zero

The zeros of a function f(x) are the values of x that cause f(x) to be equal to zero.

Zeroes

The zeroes of a function f(x) are the values of x that cause f(x) to be equal to zero.

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Difficulty Level:
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Date Created:
Mar 12, 2013
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