# 6.12: Finding Imaginary Solutions

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**Practice**Fundamental Theorem of Algebra

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Complex Conjugate

Complex conjugates are pairs of complex binomials. The complex conjugate of is . 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 .conjugate pairs theorem

The conjugate pairs theorem states that if is a polynomial of degree , with and with real coefficients, and if , where , then . Where is the complex conjugate of .fundamental theorem of algebra

The fundamental theorem of algebra states that if is a polynomial of degree , then has at least one zero in the complex number domain. In other words, there is at least one complex number such that . The theorem can also be stated as follows: an degree polynomial with real or complex coefficients has, with multiplicity, exactly complex roots.Imaginary Number

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

An imaginary number is a number that can be written as the product of a real number and .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 are the values of that cause to be equal to zero.Zeroes

The zeroes of a function are the values of that cause to be equal to zero.### Image Attributions

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This lesson shows you how to find any solution, including imaginary ones, to a polynomial.

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Date Created:

Mar 12, 2013
Last Modified:

Sep 07, 2016
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