Question

solve. |z + 4| = |z - 8|

Explanation:

Step1: Square both sides

$(z + 4)^2=(z - 8)^2$

Step2: Expand both sides

$z^{2}+8z + 16=z^{2}-16z + 64$

Step3: Subtract $z^{2}$ from both sides

$8z + 16=-16z+64$

Step4: Add $16z$ to both sides

$8z+16z + 16=-16z+16z + 64$
$24z+16 = 64$

Step5: Subtract 16 from both sides

$24z+16-16=64 - 16$
$24z=48$

Step6: Divide both sides by 24

$z=\frac{48}{24}$
$z = 2$

Answer:

$z = 2$