(-2*(-j))-(-3-j)(0.707-0.707j)=0

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Solution for (-2*(-j))-(-3-j)(0.707-0.707j)=0 equation:


Simplifying
(-2(-1j)) + -1(-3 + -1j)(0.707 + -0.707j) = 0

Remove parenthesis around (-1j)
(-2 * -1j) + -1(-3 + -1j)(0.707 + -0.707j) = 0

Multiply -2 * -1
(2j) + -1(-3 + -1j)(0.707 + -0.707j) = 0

Multiply (-3 + -1j) * (0.707 + -0.707j)
(2j) + -1(-3(0.707 + -0.707j) + -1j * (0.707 + -0.707j)) = 0
(2j) + -1((0.707 * -3 + -0.707j * -3) + -1j * (0.707 + -0.707j)) = 0
(2j) + -1((-2.121 + 2.121j) + -1j * (0.707 + -0.707j)) = 0
(2j) + -1(-2.121 + 2.121j + (0.707 * -1j + -0.707j * -1j)) = 0
(2j) + -1(-2.121 + 2.121j + (-0.707j + 0.707j2)) = 0

Combine like terms: 2.121j + -0.707j = 1.414j
(2j) + -1(-2.121 + 1.414j + 0.707j2) = 0
(2j) + (-2.121 * -1 + 1.414j * -1 + 0.707j2 * -1) = 0
(2j) + (2.121 + -1.414j + -0.707j2) = 0

Reorder the terms:
2.121 + (2j) + -1.414j + -0.707j2 = 0

Combine like terms: (2j) + -1.414j = 0.586j
2.121 + 0.586j + -0.707j2 = 0

Solving
2.121 + 0.586j + -0.707j2 = 0

Solving for variable 'j'.

Begin completing the square.  Divide all terms by
-0.707 the coefficient of the squared term: 

Divide each side by '-0.707'.
-3 + -0.828854314j + j2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -0.828854314j + 3 + j2 = 0 + 3

Reorder the terms:
-3 + 3 + -0.828854314j + j2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -0.828854314j + j2 = 0 + 3
-0.828854314j + j2 = 0 + 3

Combine like terms: 0 + 3 = 3
-0.828854314j + j2 = 3

The j term is -0.828854314j.  Take half its coefficient (-0.414427157).
Square it (0.1717498685) and add it to both sides.

Add '0.1717498685' to each side of the equation.
-0.828854314j + 0.1717498685 + j2 = 3 + 0.1717498685

Reorder the terms:
0.1717498685 + -0.828854314j + j2 = 3 + 0.1717498685

Combine like terms: 3 + 0.1717498685 = 3.1717498685
0.1717498685 + -0.828854314j + j2 = 3.1717498685

Factor a perfect square on the left side:
(j + -0.414427157)(j + -0.414427157) = 3.1717498685

Calculate the square root of the right side: 1.780940726

Break this problem into two subproblems by setting 
(j + -0.414427157) equal to 1.780940726 and -1.780940726.

Subproblem 1

j + -0.414427157 = 1.780940726 Simplifying j + -0.414427157 = 1.780940726 Reorder the terms: -0.414427157 + j = 1.780940726 Solving -0.414427157 + j = 1.780940726 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.414427157' to each side of the equation. -0.414427157 + 0.414427157 + j = 1.780940726 + 0.414427157 Combine like terms: -0.414427157 + 0.414427157 = 0.000000000 0.000000000 + j = 1.780940726 + 0.414427157 j = 1.780940726 + 0.414427157 Combine like terms: 1.780940726 + 0.414427157 = 2.195367883 j = 2.195367883 Simplifying j = 2.195367883

Subproblem 2

j + -0.414427157 = -1.780940726 Simplifying j + -0.414427157 = -1.780940726 Reorder the terms: -0.414427157 + j = -1.780940726 Solving -0.414427157 + j = -1.780940726 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.414427157' to each side of the equation. -0.414427157 + 0.414427157 + j = -1.780940726 + 0.414427157 Combine like terms: -0.414427157 + 0.414427157 = 0.000000000 0.000000000 + j = -1.780940726 + 0.414427157 j = -1.780940726 + 0.414427157 Combine like terms: -1.780940726 + 0.414427157 = -1.366513569 j = -1.366513569 Simplifying j = -1.366513569

Solution

The solution to the problem is based on the solutions from the subproblems. j = {2.195367883, -1.366513569}

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