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anonymous
 4 years ago
What is the relationship between a complex number and its conjugate?
and what is the usefulness of the conjugate and its effect on other complex numbers?
anonymous
 4 years ago
What is the relationship between a complex number and its conjugate? and what is the usefulness of the conjugate and its effect on other complex numbers?

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mathmate
 4 years ago
Best ResponseYou've already chosen the best response.0The conjugate of a complex number is that the sign of the complex component is inverted. For example, the conjugate of a+bi is abi. One significance is that the product of a complex number with its conjugate is always real.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so what exactly is the relationship? a real number?

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.0\( (a+bi)(abi)=a^2+b^2 \) The result is a real number for all values of a and b.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0how can i put that into words?

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.0You can expand the last sentence of my first response. Post your version if you're not sure.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0"the complex number and its conjugate have a set of real numbers in common"

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.0I would put it as the product of a complex and its conjugate is real. This is useful in "rationalizing" complex numbers where the denominator is a complex number. \[\frac{2+3i}{3+4i} = \frac{(2+3i)(34i)}{(3+4i)(34i)}=\frac{18+i}{25}\] This facilitates manipulation (such as addition) of complex numbers.
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