Three complex number \(a,b,c\) are called affinely independent if whenever \(t,s,u\) are real numbers such that \(ta+sb+uc = 0\) and \(t+s+u=0\), we have that \(t=s=u=0\). Show that three complex numbers \(a,b,c\) are affinely independent if and only if they are not collinear.