I passed across this chart on the web and got confused. The diagram implies that there are numbers that are neither real nor imaginary. Is that possible, or is it just an incorrect diagram?
I understand the box titled "Imaginary numbers", might actually mean to say "Pure imaginary numbers"? But even then, it implies that all real numbers are imaginary (as there are examples like 4 + 2i under complex numbers, which are imaginary), which is nonsense! Kindly help me. Thank you!
Best Answer
A complex number is the sum of a pure imaginary number and a real number. However, there are numbers which are neither real or imaginary: Octonions.
EDIT:
As the comments pointed out, I skipped quaternions, but octonions are so much cooler. If you are looking for even more numbers to bend your brain, there are the surreal numbers and the transfinite numbers.