How to represent the following system function in a block diagram?
It is a simple first-order recursive system like this:



In your case $b[0]=1$, $b[1]=0$, and $a[1]=-0.3(1+j)$. Of course the coefficient is complex if your system is complex. What you can do is split the real and imaginary parts and get two real-valued systems. The output of one is the real part of the output signal $y[n]$, and the output of the other is the imaginary part:

$$y_R[n]=0.3y_R[n-1]-0.3y_I[n-1]+x_R[n]\\
y_I[n]=0.3y_R[n-1]+0.3y_I[n-1]+x_I[n]$$

where $y_R[n]$ and $y_I[n]$ are the real and imaginary parts of $y[n]$, respectively (and the same for $x[n]$). If the input signal is real-valued then of course $x_I[n]=0$.

As for general complex-valued systems also have a look at this figure from the textbook Digital Communication by Lee and Messerschmitt: