Communication system capable of reducing power consumption, image forming apparatus, and method of controlling image forming apparatus

A communication system comprising:

• an image forming apparatus operable in a first power mode and a second power mode in which power consumption is lower than power consumption in the first power mode and greater than power consumption in a power off state;
• and
• an image processing apparatus operable in a third power mode and a fourth power mode in which power consumption is lower than power consumption in the third power mode;
• wherein the image forming apparatus includes:
• a plurality of wake-up devices, each of the plurality of wake-up devices outputs a wake-up signal;
• a first controller that receives the wake-up signal, shifts the image forming apparatus from the second power mode to the first power mode based on the wake-up signal, and identifies a wake-up device which output the received wake-up signal;
• and
• a first network interface that transmits a predetermined instruction to the image processing apparatus in a case where the identified wake-up device is a predetermined device,
• wherein the image processing apparatus includes:
• a second network interface that receives the predetermined instruction from the image forming apparatus;
• and
• a second controller that shifts the image processing apparatus from the fourth power mode to the third power mode based on the predetermined instruction, and
• wherein one of the plurality of wake-up devices is a modem, and the first network interface does not transmit the predetermined instruction to the image processing apparatus on the basis that the identified wake-up device is the modem.