What is the complex number z from identity 3z-18z'=12+i?

We'll consider z' as being the conjugate of z, therefore z
= a + bi and z' = a - bi.

We'll replace z and z' by its
rectangular forms, into the given identity:

3(a+bi) - 18(a
- bi) = 12 + i

We'll remove the
brackets:

3a + 3bi - 18a + 18bi = 12 +
i

We'll combine real parts and imaginary parts form the
left side:

-15a + 21bi = 12 +
i

Comparing, we'll get:

-15a =
12 => a = 12/-15 => a = -4/5

21b = 1
=> b = 1/21

The requesed complex
number is: z = -4/5 + i/21.