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Simplifying
j2 + -3.5j + 1.5 = 0

Reorder the terms:
1.5 + -3.5j + j2 = 0

Solving
1.5 + -3.5j + j2 = 0

Solving for variable 'j'.

Begin completing the square.

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -3.5j + -1.5 + j2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -3.5j + j2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -3.5j + j2 = 0 + -1.5
-3.5j + j2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-3.5j + j2 = -1.5

The j term is -3.5j.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5j + 3.0625 + j2 = -1.5 + 3.0625

Reorder the terms:
3.0625 + -3.5j + j2 = -1.5 + 3.0625

Combine like terms: -1.5 + 3.0625 = 1.5625
3.0625 + -3.5j + j2 = 1.5625

Factor a perfect square on the left side:
(j + -1.75)(j + -1.75) = 1.5625

Calculate the square root of the right side: 1.25

Break this problem into two subproblems by setting 
(j + -1.75) equal to 1.25 and -1.25.

Subproblem 1

j + -1.75 = 1.25 Simplifying j + -1.75 = 1.25 Reorder the terms: -1.75 + j = 1.25 Solving -1.75 + j = 1.25 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + j = 1.25 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + j = 1.25 + 1.75 j = 1.25 + 1.75 Combine like terms: 1.25 + 1.75 = 3 j = 3 Simplifying j = 3

Subproblem 2

j + -1.75 = -1.25 Simplifying j + -1.75 = -1.25 Reorder the terms: -1.75 + j = -1.25 Solving -1.75 + j = -1.25 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + j = -1.25 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + j = -1.25 + 1.75 j = -1.25 + 1.75 Combine like terms: -1.25 + 1.75 = 0.5 j = 0.5 Simplifying j = 0.5

Solution

The solution to the problem is based on the solutions from the subproblems. j = {3, 0.5}
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