(4+-9i)(41+9i)=0

Solution for (4+-9i)(41+9i)=0 equation:

(4+-9i)(41+9i)=0

We add all the numbers together, and all the variables

(-9i)(9i+41)=0

We multiply parentheses ..

(-81i^2-369i)=0

We get rid of parentheses

-81i^2-369i=0

a = -81; b = -369; c = 0;
Δ = b2-4ac
Δ = -3692-4·(-81)·0
Δ = 136161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{136161}=369$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-369)-369}{2*-81}=\frac{0}{-162}
=0
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-369)+369}{2*-81}=\frac{738}{-162}
=-4+5/9
$