(3+9i)(-3+9i)=0

Solution for (3+9i)(-3+9i)=0 equation:

(3+9i)(-3+9i)=0

We add all the numbers together, and all the variables

(9i+3)(9i-3)=0

We use the square of the difference formula

81i^2-9=0

a = 81; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·81·(-9)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54}{2*81}=\frac{-54}{162}
=-1/3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54}{2*81}=\frac{54}{162}
=1/3
$