first, real analysis != complex analysis.
secondly, analysis is the basis for calculus and physics pretty much ia a giant heap of partial differential equations
you don't have to take analysis to use calculus and do physics, but you'll be a better physicist by knowing your theory well.
also, things like contour integrals show up frequently enough that it's good to understand the math.
finally, simulation and numerical calculation is ubiquitous in physics, and understanding how things converge can really help out
