Determine the complex number z satisfying the equation $2z - 3 \overline{z} = -7 + 2i$. Note that denotes the conjugate of z.
2(a + bi) - 3 ( a - bi) = -7 + 2i
-a + 5bi = -7 + 2i
a = 7
5bi = 2i
5b = 2
b = 2/5
z = 7 + (2/5) i
