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

answer: what are the following choices