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Simplifying j + -2(1 + -2j) = 3(j + -3) + 5 j + (1 * -2 + -2j * -2) = 3(j + -3) + 5 j + (-2 + 4j) = 3(j + -3) + 5 Reorder the terms: -2 + j + 4j = 3(j + -3) + 5 Combine like terms: j + 4j = 5j -2 + 5j = 3(j + -3) + 5 Reorder the terms: -2 + 5j = 3(-3 + j) + 5 -2 + 5j = (-3 * 3 + j * 3) + 5 -2 + 5j = (-9 + 3j) + 5 Reorder the terms: -2 + 5j = -9 + 5 + 3j Combine like terms: -9 + 5 = -4 -2 + 5j = -4 + 3j Solving -2 + 5j = -4 + 3j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-3j' to each side of the equation. -2 + 5j + -3j = -4 + 3j + -3j Combine like terms: 5j + -3j = 2j -2 + 2j = -4 + 3j + -3j Combine like terms: 3j + -3j = 0 -2 + 2j = -4 + 0 -2 + 2j = -4 Add '2' to each side of the equation. -2 + 2 + 2j = -4 + 2 Combine like terms: -2 + 2 = 0 0 + 2j = -4 + 2 2j = -4 + 2 Combine like terms: -4 + 2 = -2 2j = -2 Divide each side by '2'. j = -1 Simplifying j = -1
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