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Simplifying j + -2(1 + -2j) = (39j + -3) + 5 j + (1 * -2 + -2j * -2) = (39j + -3) + 5 j + (-2 + 4j) = (39j + -3) + 5 Reorder the terms: -2 + j + 4j = (39j + -3) + 5 Combine like terms: j + 4j = 5j -2 + 5j = (39j + -3) + 5 Reorder the terms: -2 + 5j = (-3 + 39j) + 5 Remove parenthesis around (-3 + 39j) -2 + 5j = -3 + 39j + 5 Reorder the terms: -2 + 5j = -3 + 5 + 39j Combine like terms: -3 + 5 = 2 -2 + 5j = 2 + 39j Solving -2 + 5j = 2 + 39j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-39j' to each side of the equation. -2 + 5j + -39j = 2 + 39j + -39j Combine like terms: 5j + -39j = -34j -2 + -34j = 2 + 39j + -39j Combine like terms: 39j + -39j = 0 -2 + -34j = 2 + 0 -2 + -34j = 2 Add '2' to each side of the equation. -2 + 2 + -34j = 2 + 2 Combine like terms: -2 + 2 = 0 0 + -34j = 2 + 2 -34j = 2 + 2 Combine like terms: 2 + 2 = 4 -34j = 4 Divide each side by '-34'. j = -0.1176470588 Simplifying j = -0.1176470588
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