Iknow that real numbers consist of the natural or counting numbers, whole numbers, integers, rational numbers and irrational numbers. but what about imaginary number i. and is it possible that i can use an imaginary number for a real number.

The imaginary unit belongs to the set of complex numbers, denoted by . These numbers take the form , where are any real numbers.

The set of real numbers, , is a subset of , where each number in can be obtained by taking and letting be any real number.

But any number in with non-zero imaginary part is not a real number. This includes .

I'm not sure what you mean by this part of your question. It is possible to represent any real number as a complex number, but not a purely imaginary one. All real numbers are complex, but not all complex numbers are real. For example, 2 is real and complex because .

There are some operations that you can carry out on purely imaginary numbers to get a purely real number. A famous example is raising to the -th power. Since , we have

step-by-step explanation:

try remembering the steps

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: