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Simplifying 3[2 + -1(3j + -6)] + 4[6] + -1(1 + -2j) = 4 + -5j Reorder the terms: 3[2 + -1(-6 + 3j)] + 4[6] + -1(1 + -2j) = 4 + -5j 3[2 + (-6 * -1 + 3j * -1)] + 4[6] + -1(1 + -2j) = 4 + -5j 3[2 + (6 + -3j)] + 4[6] + -1(1 + -2j) = 4 + -5j Combine like terms: 2 + 6 = 8 3[8 + -3j] + 4[6] + -1(1 + -2j) = 4 + -5j [8 * 3 + -3j * 3] + 4[6] + -1(1 + -2j) = 4 + -5j [24 + -9j] + 4[6] + -1(1 + -2j) = 4 + -5j Multiply 4 * 6 24 + -9j + 24 + -1(1 + -2j) = 4 + -5j 24 + -9j + 24 + (1 * -1 + -2j * -1) = 4 + -5j 24 + -9j + 24 + (-1 + 2j) = 4 + -5j Reorder the terms: 24 + 24 + -1 + -9j + 2j = 4 + -5j Combine like terms: 24 + 24 = 48 48 + -1 + -9j + 2j = 4 + -5j Combine like terms: 48 + -1 = 47 47 + -9j + 2j = 4 + -5j Combine like terms: -9j + 2j = -7j 47 + -7j = 4 + -5j Solving 47 + -7j = 4 + -5j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '5j' to each side of the equation. 47 + -7j + 5j = 4 + -5j + 5j Combine like terms: -7j + 5j = -2j 47 + -2j = 4 + -5j + 5j Combine like terms: -5j + 5j = 0 47 + -2j = 4 + 0 47 + -2j = 4 Add '-47' to each side of the equation. 47 + -47 + -2j = 4 + -47 Combine like terms: 47 + -47 = 0 0 + -2j = 4 + -47 -2j = 4 + -47 Combine like terms: 4 + -47 = -43 -2j = -43 Divide each side by '-2'. j = 21.5 Simplifying j = 21.5
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