If the incoming signal to the mixer is 3 600 kHz and the first IF is 9 MHz, at which one of the following frequencies would the local oscillator (LO) operate?

In a mixer, the intermediate frequency (IF) is the mathematical difference or sum of the incoming radio frequency (RF) and the local oscillator (LO) frequency. The relationship can be expressed as IF = |RF - LO| or IF = RF + LO. Given an incoming signal (RF) of 3 600 kHz and an IF of 9 000 kHz (9 MHz), we can calculate the possible LO frequencies. To find the LO that produces a difference of 9 000 kHz, we calculate: LO = IF - RF (9 000 - 3 600 = 5 400 kHz) or LO = IF + RF (9 000 + 3 600 = 12 600 kHz). Looking at the provided options, 5 400 kHz is the only correct mathematical match. The other options are results of incorrect arithmetic or misapplications of the mixing formula.