How to remotely turn on HP mini from IPhone?

I have been trying to figure out how to remotely turn on or wake my HP mini from my iPhone so that I can work on it but every time I look up how to do it either cost me money but still doesn't or the tech terms are too complicated to understand. So I guess what I'm asking for is a free (or really cheap) way to turn on my computer remotely with instructions that are easy to understand.

As a laptop or netbook device, I suspect that there's no way of starting it from a powered off state without physically pressing the power button.

Remote wake up requires that the network interface that is going to receive the wake up call has to be powered up and able to recognise a wake up packet. On a desktop machine, this is achieved by keeping the Ethernet adapter powered up while the main part of the computer is powered down. Normally wake up by wireless is not supported.

I doubt whether the iPhone will send a wake up packet to a Windows computer, especially as I believe the iPhone uses wireless networking and if the HP supports wake up, it will probably be by Ethernet.