I was reading the first proof here on exponential martingale, https://fabricebaudoin.wordpress.com/2012/09/27/lecture-23-time-changed-martingales-and-planar-brownian-motion/
It says that
"Let $
N_t=e^{i\lambda M_t +\frac{1}{2}\lambda^2 t}$. By using Ito’s formula, we obtain that for $s \le t, N_t =N_s +\int_s^t N_u dM_u.$"
I tried working out the same thing using Ito's formula but what i got was $N_t =N_s +i\lambda\int_s^t N_u dM_u.$
I have the extra $i\lambda$ popping up in front of the integral, can someone help see what i might be doing wrong?
Many Thanks!