how do you solve a complex numbers questions where z conjugate+2z = -4-4i+10+3i, where you want to solve for z

Question

anonymous · Answer

dY=dX + ZdX + XdZ-2*ZdZ. =(1+Z)dX + (X-2Z)dZ. 3.2) Y=40 + 3X + 4XZ. 2. dY=3dX + 4Z. 2. dX + 8XZdZ. = (3+4Z. 2 ). dX +8XZdZ. 3.3) For 3.1),

anonymous · Answer

what is dY?

helder_edwin · Answer

$$ \large \overline{z}+2z=-4-4i+10+3i=6-i $$

let $z=a+ib$ so $\overline{z}=a-ib$ then
$$ \large 6-i=\overline{z}+2z=(a-ib)+2(a+ib)=3a+ib $$
so $3a=6$ and $b=-1$ and from this $a=2$ and $b=-1$ therefore
$$ \large z=2-i $$

anonymous · Answer

THANK YOU SO MUCH