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**1. Homework Statement**

Find all complex solutions to the following equation:

[tex]3(x^2 + y^2) + (x - iy)^2 + 2(x + iy) = 0 [/tex]

**2. Homework Equations**

I want to use the quadratic formula, but not sure if it applies here.

**3. The Attempt at a Solution**

This is as far as I can get. What I would like is some idea as to what technique to solve this.