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Simplifying 2.6(j + -1) + 0.7 = 1.2(3 + -1j) + 0.2 Reorder the terms: 2.6(-1 + j) + 0.7 = 1.2(3 + -1j) + 0.2 (-1 * 2.6 + j * 2.6) + 0.7 = 1.2(3 + -1j) + 0.2 (-2.6 + 2.6j) + 0.7 = 1.2(3 + -1j) + 0.2 Reorder the terms: -2.6 + 0.7 + 2.6j = 1.2(3 + -1j) + 0.2 Combine like terms: -2.6 + 0.7 = -1.9 -1.9 + 2.6j = 1.2(3 + -1j) + 0.2 -1.9 + 2.6j = (3 * 1.2 + -1j * 1.2) + 0.2 -1.9 + 2.6j = (3.6 + -1.2j) + 0.2 Reorder the terms: -1.9 + 2.6j = 3.6 + 0.2 + -1.2j Combine like terms: 3.6 + 0.2 = 3.8 -1.9 + 2.6j = 3.8 + -1.2j Solving -1.9 + 2.6j = 3.8 + -1.2j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1.2j' to each side of the equation. -1.9 + 2.6j + 1.2j = 3.8 + -1.2j + 1.2j Combine like terms: 2.6j + 1.2j = 3.8j -1.9 + 3.8j = 3.8 + -1.2j + 1.2j Combine like terms: -1.2j + 1.2j = 0.0 -1.9 + 3.8j = 3.8 + 0.0 -1.9 + 3.8j = 3.8 Add '1.9' to each side of the equation. -1.9 + 1.9 + 3.8j = 3.8 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + 3.8j = 3.8 + 1.9 3.8j = 3.8 + 1.9 Combine like terms: 3.8 + 1.9 = 5.7 3.8j = 5.7 Divide each side by '3.8'. j = 1.5 Simplifying j = 1.5
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