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Simplifying 5.6 + 13.2j + -17.92 = 9(0.5j + -19.75) + 1 Reorder the terms: 5.6 + -17.92 + 13.2j = 9(0.5j + -19.75) + 1 Combine like terms: 5.6 + -17.92 = -12.32 -12.32 + 13.2j = 9(0.5j + -19.75) + 1 Reorder the terms: -12.32 + 13.2j = 9(-19.75 + 0.5j) + 1 -12.32 + 13.2j = (-19.75 * 9 + 0.5j * 9) + 1 -12.32 + 13.2j = (-177.75 + 4.5j) + 1 Reorder the terms: -12.32 + 13.2j = -177.75 + 1 + 4.5j Combine like terms: -177.75 + 1 = -176.75 -12.32 + 13.2j = -176.75 + 4.5j Solving -12.32 + 13.2j = -176.75 + 4.5j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-4.5j' to each side of the equation. -12.32 + 13.2j + -4.5j = -176.75 + 4.5j + -4.5j Combine like terms: 13.2j + -4.5j = 8.7j -12.32 + 8.7j = -176.75 + 4.5j + -4.5j Combine like terms: 4.5j + -4.5j = 0.0 -12.32 + 8.7j = -176.75 + 0.0 -12.32 + 8.7j = -176.75 Add '12.32' to each side of the equation. -12.32 + 12.32 + 8.7j = -176.75 + 12.32 Combine like terms: -12.32 + 12.32 = 0.00 0.00 + 8.7j = -176.75 + 12.32 8.7j = -176.75 + 12.32 Combine like terms: -176.75 + 12.32 = -164.43 8.7j = -164.43 Divide each side by '8.7'. j = -18.9 Simplifying j = -18.9
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