The ideal operational amplifier is a modelling abstraction used to simplify circuit analysis. Among its defining assumptions, the most relevant here is infinite input impedance between its two input terminals. Input impedance is the opposition the amplifier presents to any current trying to enter its inputs; if that impedance is infinite, then by Ohm's law the current is voltage divided by an infinitely large resistance, which is effectively zero.

This gives one of the two 'golden rules' used to analyse op-amp circuits: no current flows into (or out of) the input terminals, so the inputs behave like an open circuit. (The companion rule, valid with negative feedback, is that the two inputs sit at virtually the same voltage.)

The full set of ideal op-amp properties is:

• Infinite input impedance → zero input current, which is exactly what the question asks about.
• Zero output impedance → it can drive any load without its output voltage sagging.
• Infinite open-loop gain.
• Infinite bandwidth and zero offset.

Why the other pairings fail: a fixed 1 milliampere or 1 ampere of input current would require finite (indeed small) input impedance, contradicting the ideal model, so the pairings tying a real current to zero or moderate impedance are wrong. Likewise, the input current of an ideal op-amp is a property of its infinite impedance, not something that scales with the supply voltage. Only zero current with infinite input impedance is self-consistent.