Say my quantum register is of size $3$ qubits. This means I'll need $2^3$ complex numbers to describe all of its possible arrangements. But each complex number requires $2$ real numbers, so maybe I could say I'll need $2^{3}\times2 = 2^4$ real numbers. Is this correct?
Granted, a complex number is a number. But when we implement a complex number on any classical computer, we always reserve two numbers for it. A complex number is a number, but down to computer technology it really is a pair of numbers. When it comes to storing information, the matter is more about technology than abstract science.
I know in complexity theory it doesn't matter if $2^{N}$ or $2^{N+1}$, but I haven't seen any mention of this little detail anywhere and I've been reading every introduction on quantum computing I can find. Please do mention any source that you might know that has touched on this little technicality. Thank you!