Question

I know 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.

Answer 1

The imaginary unit
`i` belongs to the set of complex numbers, denoted by
`\mathbb C`. These numbers take the form
`a+bi`, where
`a,b` are any real numbers.

The set of real numbers,
`\mathbb R`, is a subset of
`\mathbb C`, where each number in
`\mathbb R` can be obtained by taking
`b=0` and letting
`a` be any real number.

But any number in
`\mathbb C` with non-zero imaginary part is not a real number. This includes
`i`.

• "is it possible that i can use an imaginary number for a real number"

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
`2=2+0i`.

There are some operations that you can carry out on purely imaginary numbers to get a purely real number. A famous example is raising
`i` to the
`i`-th power. Since
`i=e^(i\pi/2)`, we have

`i^i=\left(e^(i\pi/2)\right)^i=e^(i^2\pi/2)=e^(-\pi/2)\approx0.2079`