j=-j(0.707-0.707j)

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

j=-j(0.707-0.707j)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(-j(-0.707j+0.707)), so:

-j(-0.707j+0.707)

We multiply parentheses

-0j^2-0.707j

We add all the numbers together, and all the variables

-1j^2-0.707j

Back to the equation:

-(-1j^2-0.707j)


We get rid of parentheses

1j^2+0.707j+j=0

We add all the numbers together, and all the variables

j^2+1.707j=0

a = 1; b = 1.707; c = 0;
Δ = b2-4ac
Δ = 1.7072-4·1·0
Δ = 2.913849
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{-(1.707)-\sqrt{2.913849}}{2*1}=\frac{-1.707-\sqrt{2.913849}}{2}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.707)+\sqrt{2.913849}}{2*1}=\frac{-1.707+\sqrt{2.913849}}{2}
$