# What is i to the power of i?

When you first learnt that , you have entered the mysterious world of complex numbers.

A mystifying question would be to ask, what is i to the power of i? Is it a complex number?

The surprising answer is that is a real number! Let us explain it here:

The key step is to use Euler’s formula: . This has been voted as the most beautiful equation in mathematics by many people.

Then,

Hence,

It is really amazing that an imaginary number to the power of an imaginary number gives a real number, isn’t it? Leave your comments below!