(-3-j)(0.707-0.707j)=0

Solution for (-3-j)(0.707-0.707j)=0 equation:

(-3-j)(0.707-0.707j)=0

We add all the numbers together, and all the variables

(-1j-3)(-0.707j+0.707)=0

We multiply parentheses ..

(+0j^2-0.707j+0j-2.121)=0

We get rid of parentheses

0j^2-0.707j+0j-2.121=0

We add all the numbers together, and all the variables

j^2+0.293j-2.121=0

a = 1; b = 0.293; c = -2.121;
Δ = b2-4ac
Δ = 0.2932-4·1·(-2.121)
Δ = 8.569849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.293)-\sqrt{8.569849}}{2*1}=\frac{-0.293-\sqrt{8.569849}}{2}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.293)+\sqrt{8.569849}}{2*1}=\frac{-0.293+\sqrt{8.569849}}{2}
$