Math what is i

And you could actually derive that even from this definition, but this is pretty straight forward; anything to the zeroth power, including "i" is one. Then you say, ok, what is "i" to the first power, well anything to the first power is just that number times itself once. So that's justgoing to be "i". Really by the definition of what it means to take an exponent, so that completely makes sense. And then you have "i" to the second power. Lets try "i" to the third power ill do this in a color i haven't used.

This is the same thing as this, which is the same thing as that, "i" squared is negative one. So you multiply it out, negative one times "i" equals negative "i". Now what happens when you take "i" to the fourth power, I'll do it up here. Well once again this is going to be "i" times "i" to the third power. So that's "i" times "i" to the third power. And so "i" times "i" would get negative one, but you have a negative out here, so its "i" times "i" is negative one, and you have a negative, that gives you positive one.

Let me write it out. This is the same thing as, so this is "i" times negative "i", which is the same thing as negative one times, remember multiplication is commutative, if you're multiplying a bunch of numbers you can just switch the order. This is the same thing as negative one times "i" times "i".

Negative one times negative one is equal to positive one. So "i" to the fourth is the same thing as "i" to the zeroth power. Now lets try "i" to the fifth.

Well that's just going to be "i" to to the fourth times "i". The Unit Imaginary Number, i , has an interesting property. It "cycles" through 4 different values each time we multiply:. And that leads us into another topic, the complex plane :. Example: What is 5 i 2? Example What is i 10? An Imaginary Number, when squared , gives a negative result. Mazur, B. New York: Farrar, Straus and Giroux, Sloane, N.

Uhler, S. Monthly 28 , , Wells, D. Middlesex, England: Penguin Books, p. Weisstein, Eric W. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.

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