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Simplifying j(5 + -3j) = 7j + 4 (5 * j + -3j * j) = 7j + 4 (5j + -3j2) = 7j + 4 Reorder the terms: 5j + -3j2 = 4 + 7j Solving 5j + -3j2 = 4 + 7j Solving for variable 'j'. Reorder the terms: -4 + 5j + -7j + -3j2 = 4 + 7j + -4 + -7j Combine like terms: 5j + -7j = -2j -4 + -2j + -3j2 = 4 + 7j + -4 + -7j Reorder the terms: -4 + -2j + -3j2 = 4 + -4 + 7j + -7j Combine like terms: 4 + -4 = 0 -4 + -2j + -3j2 = 0 + 7j + -7j -4 + -2j + -3j2 = 7j + -7j Combine like terms: 7j + -7j = 0 -4 + -2j + -3j2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 2j + 3j2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 2j + 3j2)' equal to zero and attempt to solve: Simplifying 4 + 2j + 3j2 = 0 Solving 4 + 2j + 3j2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 0.6666666667j + j2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 0.6666666667j + -1.333333333 + j2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 0.6666666667j + j2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 0.6666666667j + j2 = 0 + -1.333333333 0.6666666667j + j2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 0.6666666667j + j2 = -1.333333333 The j term is 0.6666666667j. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667j + 0.1111111112 + j2 = -1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667j + j2 = -1.333333333 + 0.1111111112 Combine like terms: -1.333333333 + 0.1111111112 = -1.2222222218 0.1111111112 + 0.6666666667j + j2 = -1.2222222218 Factor a perfect square on the left side: (j + 0.3333333334)(j + 0.3333333334) = -1.2222222218 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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