I kinda gave up on the last problem... so new problem :)
Let \(a = 4 + 3i,\) \(b = 1 2i,\)and \(c = 8  5i.\) The complex number d is such that a, b, c, and d form the vertices of a parallelogram, when plotted in the complex plane. Enter all possible values of d, separated by commas.
I found three different possible values of d using this graph:
https://www.desmos.com/calculator/cwbrobjoav
You can turn on the different parallelograms by clicking the circle next to the name.
Here's a picture with all of them turned on:
The different possible values of d are: 

3 + 6i 

5  10i 

11 + 0i 
Let \(\large{a = 4 + 3i}\), \(\large{b = 1 2i}\), and \(\large{c = 8  5i}\).
The complex number d is such that a, b, c, and d form the vertices of a parallelogram,
when plotted in the complex plane. Enter all possible values of d, separated by commas.
\(\begin{array}{rclclcl} \hline \mathbf{d} &=& a+b+c &=& (4+3i)+ (1 2i) + (8  5i) &=& \mathbf{510i} \\\\ \mathbf{d} &=& ab+c &=& (4+3i) (1 2i) + (8  5i) &=& \mathbf{11+0i} \\\\ \mathbf{d} &=& a+bc &=& (4+3i)+ (1 2i)  (8  5i) &=& \mathbf{3+6i} \\ \hline \end{array} \)