Determine the complex number satisfying the equation​

Um... I'm only in 7th grade so I just going to solve WITHOUT the complex conjugate and Zbar thingy just for the fun of it.

1. Sqaure both sides.

9z^2-4z^2=1+8

9z^2-4z^2=9

5z^2=9

z^2=9/5

$\boxed{z=\frac{\sqrt{9}}{5}}$

3z + 4iz'  = 1 - 8i

3 (a + bi) + 4i(a - bi)   = 1 - 8i

3a + 3bi + 4ai + 4b  = 1 - 8i

3a+ 4b =  1      ⇒   12a + 16b  = 4

4a + 3b  = - 8 ⇒     -12a - 9b = 24

7b  = 28

b = 4        and   3a + 4(4) = 1   ⇒  3a = - 15  ⇒  a = -5

So

z = -5 + 4i