How can we show that if $E\to M$ is a smooth orientable rank two vector bundle over a smooth manifold then $E$ has a complex structure?
This is Exercise 2.3 of https://www.mathematik.hu-berlin.de/~wendl/pub/rationalRuled.pdf, and above the statement it is written that this exercise depends on the fact that certain spaces of complex structures are nonempty and contractible. But I have no idea about what does "certain space" mean here. Any hints?