Imaginary Numbers - YourTeacher.com - Algebra 2 Help

For a complete lesson on imaginary numbers, go to http://www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that the imaginary number "i" is equal to the square root of -1, which means that i^2 is equal to (the square root of -1) squared, which equals -1. Students also learn to simplify imaginary numbers. For example, to simplify the square root of -81, think of it as the square root of -1 times the square root of 81, which simplifies to i times 9, or 9i. To simplify 11/8i, the first step is to get rid of the "i" in the denominator by multiplying both the numerator and the denominator of the fraction by i, to get 11i/8i^2, and remember that i^2 = -1, so we have 11i/8(-1), or 11i/-8, or -11i/8.

Category:

Education

Tags:

• imaginary
• numbers
• example
• pure
• square
• root
• negative
• one

[scout6686]

this chick is more nerd than I can take.

[NeuterSkooter]

Why learn something that isn't real!

[VoguishArts]

@Balticmania The internet is a great source for learning right? You learn and actually hold more knowledge, rather than in a school being taught by some moron trying to make a living with ease.

[waynemv]

@bandet888

P.S. the imaginary number j used in electronics is actually the negative of the imaginary number i used in algebra. So if anywhere you see a j you replace it with -i, the math will still work out just the same. :-)

[waynemv]

@bandet888 Some people may try to tell you that i*j=k. Then they'll tell you j*i=-k. Seriously, the one has a negative sign and the other doesn't? Could mathematics be any more messed up than that?* Anyway, see the Wikipedia page titled "Quaternion" for more examples of their noncommutative insanity!

*The answer is yes, see octernions.

[waynemv]

@mogeroithe Complex numbers are necessary in order to have a complete system of algebra. Complex numbers had to be introduced because equations that were written using only real numbers would sometimes turn out to have solutions that are not real numbers.

Also historically, when mathematicians tried to solve some third degree polynomials, it was discovered that although the solutions were real numbers, the equations could only be solved by using complex numbers during the intermediate steps!

[waynemv]

@mogeroithe In mathematics, the words "negative", "positive", "real", and "imaginary" are technical terms and mean only what they are defined to mean in the context, nothing more. The terms have nothing to do with whether such numbers exist in reality. How can any number be said to really exist when numbers are abstractions? Anyway, the kind of existence imaginary numbers have is no different from the kind of existence the real numbers have. If one is actual the other is too, and vice versa.

[waynemv]

Sqrt(25) = 5 and not -5. That's because the square root function is defined as selecting the positive value. But that rule fails for sqrt(-25), as neither 5i nor -5i is positive.

It is usually understood that sqrt(-25) is an improper and ill-defined notation, since it has two solutions and no rule for picking which. The i symbol was introduced for the very purpose of eliminating the need to use the square root notation for negative numbers so that this very ambiguity could be avoided.

[MetapodMaster]

the stare at the end...it looks into your soul

[TRANNSVESTITEPONY]

@scout6686 imagine how tight she'd be.

[trainedtiger]

I think she is pretty, commence hating.

[bandet888]

In high school I was taught that the imaginary number is represented by the letter i (for imaginary of course). But when I went to college I was taught that the imaginary number was represented by the letter j not i. Supposetly the letter i was getting confused with amps in electronice (I studied electronics) So they decided to use the next letter in the alphabet which is j.