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Context: I am creating a hard science-fiction world set in the Alpha Centauri system.
How large and bright would the binary star Alpha Centauri AB in the sky, when observed from an exoplanet (Proxima C) in Proxima Centauri? Would it be visible during the day? Is it close enough to cast any light onto the planet?
According to this page, Proxima is about 13,000 AU (or roundly 1/5 light year) from the AB pair that orbit only 23 AU apart (comparable to Neptune's orbit around the Sun). From that distance, the individual stars of AB would be, well, stars. Very bright stars (seemingly of magnitude -1 or brighter, according to this calculator, brighter than Sirius and comparable to Venus), but without any hint of a disk.
Given that Alpha A is a little bigger and 1.5 times brighter than our Sun, while Alpha B is a little smaller and a little less than half as bright (not to mention, at different temperatures, they'll be slightly different colors, one bluer and the other yellower than our Sun), they should be comparable to what our Sun would look like from the outer Kuiper belt or inner Oort cloud.
Now, the more interesting question is whether they'd be a visual binary (we'll assume vision as good as human standard): arcsin (23 / 13000) ~ 0.1 degree or about 6 minutes of arc -- 1/5 the width of the Sun or Moon as seen from Earth makes the AB system an easy visual binary as seen from Proxima B, and it would be obvious over a pretty short time (orbital period just under 80 Earth years) that the two stars orbit each other.
