This question asks why high-frequency carrier signals are used in modulation. The dominant practical reason is the physical size of the antenna required to radiate (and receive) the signal efficiently. For efficient radiation, an antenna's dimension must be comparable to the signal's wavelength — a common rule of thumb is a quarter-wavelength (λ/4) element.

Wavelength and frequency are inversely related:

λ = c / f, where c = 3 × 10⁸ m/s

Consider a baseband audio (speech) signal of about 1000 Hz. Its wavelength would be λ = (3 × 10⁸) / 1000 = 3 × 10⁵ m = 300 km, requiring a λ/4 antenna roughly 75 km long — utterly impractical.

If instead this message is modulated onto a high-frequency carrier, say 100 MHz (FM broadcast band):

λ = (3 × 10⁸) / (100 × 10⁶) = 3 m, so a λ/4 antenna is only about 0.75 m — perfectly practical. Hence the correct answer is to reduce the physical size of the required antenna.

Why the other options are wrong:

• To amplify the original message signal: modulation shifts the message to a higher frequency band; it does not add power/gain to the message. Amplification is a separate function performed by amplifiers.
• To make the signal move at the speed of light: all electromagnetic waves already travel at essentially the speed of light regardless of frequency, so the carrier frequency does not change the propagation speed.
• To eliminate the need for a receiver: a receiver is always required to demodulate and recover the message; modulation does not remove it. Modulation also enables benefits like frequency-division multiplexing and reduced antenna size — but never the elimination of the receiver.