How is Wi-Fi transmitter sends complex number to receiver?
How is transmitter send those complex numbers?

It doesn't.  As you noted, that's impossible.

What is the transmitter actually send?

The short answer is that the transmitter takes a baseband signal expressed as inphase/quadrature (I/Q), and modulates the inphase part with $\cos \omega t$ and the quadrature part as $\sin \omega t$.  On the receiving end, the inphase part is demodulated by $\cos \omega t$, and the quadrature part is demodulated by $-\sin \omega t$.
This acts as if the I/Q signal were complex with the inphase part being real and the quadrature part being imaginary, and that the transmitter modulated it with $e^{i \omega t}$, and then only transmitted the real part.
It turns out that you can work out all the inphase/quadrature math, very laboriously using only real numbers and trig identities -- or, you can note that if you pretend that your I/Q signal is complex, then you can do all the arithmetic with complex numbers and everything behaves exactly the same.