let 0>i>1

prove that (1+i)^t < 1+i*t for 0>t>1.

I am a little bit clueless where to start. At first I thought about integrating the area in between and if that area was positive then it would be true, if negative then it would be false and that would basically prove it. But it turned out to be a lot more complicated than it first seemed which led me to believe there is probably a much better way. Any help would be appreciated.