What is z if z/2 + 3=z'/3 - 2? z complex number

We'll write the rectangular form of the complex number
z:

 z = a + bi

z' is the
conjugate of z:

z' = a - bi

To
determine z, we'll have to determine it's coefficients:

(a
+ bi)/2 + 3 = (a - bi)/3 - 2

We'll multiply by 6 both
sides:

3(a + bi) + 18 = 2(a - bi) -
12

We'll remove the
brackets:

3a + 3bi + 18 = 2a - 2bi -
12

We'll move all terms to the left
side:

3a - 2a + 3bi + 2bi + 18 + 12 =
0

a + 5bi + 30 = 0

The real
part of the complex number from the left side is:

Re(z) = a
+ 30

The real part of the complex number from the right
side is:

Re(z) = 0

Comparing,
we'll get:

 a + 30 = 0

a =
-30

The imaginary part of the complex number from the left
side is:

Im(z) = 5b

The
imaginary part of the complex number from the right side
is:

Im(z) = 5b

Comparing,
we'll get:

5b = 0

b =
0

The complex number z is:
z = -30 + 0*i