(-5+9i)(-5-9i)=0

Solution for (-5+9i)(-5-9i)=0 equation:

(-5+9i)(-5-9i)=0

We add all the numbers together, and all the variables

(9i-5)(-9i-5)=0

We multiply parentheses ..

(-81i^2-45i+45i+25)=0

We get rid of parentheses

-81i^2-45i+45i+25=0

We add all the numbers together, and all the variables

-81i^2+25=0

a = -81; b = 0; c = +25;
Δ = b2-4ac
Δ = 02-4·(-81)·25
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90}{2*-81}=\frac{-90}{-162}
=5/9
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90}{2*-81}=\frac{90}{-162}
=-5/9
$