True scientist

DRUMPF BTFO

I'm a little flimsy on formal definitions, but aren't complex numbers called complex because they aren't totally real or imaginary? They are of the form a + bi where a,b are real and non-zero?

I've once heard a mathematician (on numberphile or so) say that he liked the interpretation of complex numbers to mean what complex does in chemistry. where you have e.g. aqueous complexes of metal ions. so in math you have complexes of real and imaginary numbers.

Hot

you're my kind of guy, pal

Yeah but it's not like complex numbers are the only way of doing that. Plain vectors let you have tuples of real numbers orthogonal to each other. Then there are quaternions, split-complex numbers, etc. There's nothing special about complex numbers per se.

are you taking inorganic chem? we see plenty of these octahedral coordination complexes.

Complex numbers are all numbers of the form a+ib where a,b real. Obviously this includes all real numbers and all imaginary numbers.

sqrt(-1) is not a real number. It's an imaginary or it's a complex, but it's not a real.

the sqrt(-1)=i meme is annoying, since sqrt(-1)=-i is also true, and you can't take a principle root since "take it from the positive side" doesn't really make sense for complex numbers.