First of all, by the time Alpha Centauri A becomes a red giant, it will no longer be this close to the Sun so it probably wouldn't be visible. But let's assume it does stay 4.2 ly away.

By the Stefan-Boltzmann Law, the luminosity of a star is given by

$$L = 4\pi R^2 \sigma T^4$$

Assuming a radius of $200 R_\odot$ and a temperature of $3600 \text{ K}$, we get a luminosity of about $6021 L_\odot$, compared to a present-day luminosity of $1.5 L_\odot$.

This means that the red giant would be 4014 times brighter, corresponding to an apparent magnitude increase of 9 magnitudes to about -9 apparent magnitude. This is slightly dimmer than the brightness of the moon.

First of all, by the time Alpha Centauri A becomes a red giant, it will no longer be this close to the Sun due to the orbit of the stars around the galaxy so it probably wouldn't be visible. But let's assume it does stay 4.2 ly away.

By the Stefan-Boltzmann Law, the luminosity of a star is given by

$$L = 4\pi R^2 \sigma T^4$$

Assuming a radius of $200 R_\odot$ and a temperature of $3600 \text{ K}$, we get a luminosity of about $6021 L_\odot$, compared to a present-day luminosity of $1.5 L_\odot$.

This means that the red giant would be 4014 times brighter, corresponding to an apparent magnitude increase of 9 magnitudes to about -9 apparent magnitude. This is slightly dimmer than the brightness of the moon.