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.
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!
2 thoughts on “What is i^i ?”
Reblogged this on How and Why? and commented:
imaginary powers are interesting things
Thanks for reblogging!