(-5+7j)-(-6-5j)3j=

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Solution for (-5+7j)-(-6-5j)3j= equation:


Simplifying
(-5 + 7j) + -1(-6 + -5j) * 3j = 0

Remove parenthesis around (-5 + 7j)
-5 + 7j + -1(-6 + -5j) * 3j = 0

Reorder the terms for easier multiplication:
-5 + 7j + -1 * 3j(-6 + -5j) = 0

Multiply -1 * 3
-5 + 7j + -3j(-6 + -5j) = 0
-5 + 7j + (-6 * -3j + -5j * -3j) = 0
-5 + 7j + (18j + 15j2) = 0

Combine like terms: 7j + 18j = 25j
-5 + 25j + 15j2 = 0

Solving
-5 + 25j + 15j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 5j + 3j2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-1 + 5j + 3j2)' equal to zero and attempt to solve: Simplifying -1 + 5j + 3j2 = 0 Solving -1 + 5j + 3j2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 1.666666667j + j2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.666666667j + 0.3333333333 + j2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.666666667j + j2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.666666667j + j2 = 0 + 0.3333333333 1.666666667j + j2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.666666667j + j2 = 0.3333333333 The j term is 1.666666667j. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667j + 0.6944444447 + j2 = 0.3333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667j + j2 = 0.3333333333 + 0.6944444447 Combine like terms: 0.3333333333 + 0.6944444447 = 1.027777778 0.6944444447 + 1.666666667j + j2 = 1.027777778 Factor a perfect square on the left side: (j + 0.8333333335)(j + 0.8333333335) = 1.027777778 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (j + 0.8333333335) equal to 1.013793755 and -1.013793755.

Subproblem 1

j + 0.8333333335 = 1.013793755 Simplifying j + 0.8333333335 = 1.013793755 Reorder the terms: 0.8333333335 + j = 1.013793755 Solving 0.8333333335 + j = 1.013793755 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + j = 1.013793755 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + j = 1.013793755 + -0.8333333335 j = 1.013793755 + -0.8333333335 Combine like terms: 1.013793755 + -0.8333333335 = 0.1804604215 j = 0.1804604215 Simplifying j = 0.1804604215

Subproblem 2

j + 0.8333333335 = -1.013793755 Simplifying j + 0.8333333335 = -1.013793755 Reorder the terms: 0.8333333335 + j = -1.013793755 Solving 0.8333333335 + j = -1.013793755 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + j = -1.013793755 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + j = -1.013793755 + -0.8333333335 j = -1.013793755 + -0.8333333335 Combine like terms: -1.013793755 + -0.8333333335 = -1.8471270885 j = -1.8471270885 Simplifying j = -1.8471270885

Solution

The solution to the problem is based on the solutions from the subproblems. j = {0.1804604215, -1.8471270885}

Solution

j = {0.1804604215, -1.8471270885}

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