Please help with 2 problems

\(\left|\dfrac 1 2 - c i \right| = \left(\dfrac 1 2 \right)^2 + c^2 = \dfrac 3 4\\ \dfrac 1 4 + c^2 = \dfrac 3 4\\ c^2 = \dfrac 1 2\\ c = \pm \dfrac{1}{\sqrt{2}}\)

\(2z - 3\bar{z} = -2 - 30i\\ \text{let $z=x+iy$}\\ 2x + i2y - 3x + i3y = -2 - 30i\\ -x+i5y=-2-30i\\ x = 2,~y = -6i\\ z = 2-6i\)

2) Let  z  =  a + bi

So we have

2 (a + bi)  - 3 (a - bi)   =  -2  - 30i      simplify

2a + 2bi   - 3a  + 3bi  =   -2  - 30i

-1a + 5bi =   -2 - 30i

Equate terms

-1a   = -2             5bi  = -30i

a  =  2           b  = -6

So

z =  2  -  6i