Describe all solutions to zw -3w - 2iw + 4iz = - 8 + 12i where z and w are complex numbers.

We can rearrange the equation as follows:

zw - 3w - 2iw + 4iz = -8 + 12i

(z - 4i)(w - 2i) = -8 + 12i

z - 4i = -\frac{8 + 12i}{w - 2i}

z = -\frac{8 + 12i}{w - 2i} + 4i

This is a general formula for all solutions to the equation, where z and w are complex numbers.

To find specific solutions, we can substitute in any values for w. For example, if we let w=1, then we get:

z = -\frac{8 + 12i - 8i + 8}{1 + 2}

z = -\frac{4 + 4i}{3}

Therefore, one solution is z=−34+4i​. There are infinitely many other solutions, each of which can be found by substituting in a different value for w.