Kruxx wrote:
malice wrote:
wasnt i imaginary? just like alliance guilds making it past broodlord?
he wins, something complex is real and imaginary together.
Actually real and imaginary numbers are a subset of complex numbers (this is similar to how squares are a subset of rectangles; all squares are rectangles but not all rectangles are squares). In other words all real numbers are also complex (with their imaginary parts = 0) and all imaginary numbers are also complex (with their real parts = 0). However not all complex numbers are real and not all complex numbers are imaginary.
So the original statement "i is complex" is correct. The second statement "You'd think i^i is about as complex as you can get but i^i is real" is perhaps a bit misleading or awkward (what does it mean for one number to be more complex than another?). However it is also still a correct statement.
Regardless, proving that i^i is a real number is much more interesting than arguing about semantics. One way to show this (which happens to be the way I did) involves using Euler's formula e^ix = cos(x) + isin(x).
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