6+j(0.707-0.707j)=6+0.707j-0.707j^2. That is it.
If you want to solve for j, then:
Solve for j:
-(0.707 j^2)+0.707 j+6 = 0
-(0.707 j^2)+0.707 j+6 = -(707 j^2)/1000+(707 j)/1000+6:
-(707 j^2)/1000+(707 j)/1000+6 = 0
Multiply both sides by -1000/707:
j^2-j-6000/707 = 0
Add 6000/707 to both sides:
j^2-j = 6000/707
Add 1/4 to both sides:
j^2-j+1/4 = 24707/2828
Write the left hand side as a square:
(j-1/2)^2 = 24707/2828
Take the square root of both sides:
j-1/2 = sqrt(24707/707)/2 or j-1/2 = -sqrt(24707/707)/2
Add 1/2 to both sides:
j = 1/2+sqrt(24707/707)/2 or j-1/2 = -sqrt(24707/707)/2
Add 1/2 to both sides:
Answer: | j = 1/2+sqrt(24707/707)/2 or j = 1/2-sqrt(24707/707)/2=+or- 2.4557677
