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Simplifying 15j + (-6j + 5) + -2 + -1(-1j + 3) = -1(7j + 23) + -1j + (3 + -2j) Reorder the terms: 15j + (5 + -6j) + -2 + -1(-1j + 3) = -1(7j + 23) + -1j + (3 + -2j) Remove parenthesis around (5 + -6j) 15j + 5 + -6j + -2 + -1(-1j + 3) = -1(7j + 23) + -1j + (3 + -2j) Reorder the terms: 15j + 5 + -6j + -2 + -1(3 + -1j) = -1(7j + 23) + -1j + (3 + -2j) 15j + 5 + -6j + -2 + (3 * -1 + -1j * -1) = -1(7j + 23) + -1j + (3 + -2j) 15j + 5 + -6j + -2 + (-3 + 1j) = -1(7j + 23) + -1j + (3 + -2j) Reorder the terms: 5 + -2 + -3 + 15j + -6j + 1j = -1(7j + 23) + -1j + (3 + -2j) Combine like terms: 5 + -2 = 3 3 + -3 + 15j + -6j + 1j = -1(7j + 23) + -1j + (3 + -2j) Combine like terms: 3 + -3 = 0 0 + 15j + -6j + 1j = -1(7j + 23) + -1j + (3 + -2j) 15j + -6j + 1j = -1(7j + 23) + -1j + (3 + -2j) Combine like terms: 15j + -6j = 9j 9j + 1j = -1(7j + 23) + -1j + (3 + -2j) Combine like terms: 9j + 1j = 10j 10j = -1(7j + 23) + -1j + (3 + -2j) Reorder the terms: 10j = -1(23 + 7j) + -1j + (3 + -2j) 10j = (23 * -1 + 7j * -1) + -1j + (3 + -2j) 10j = (-23 + -7j) + -1j + (3 + -2j) Remove parenthesis around (3 + -2j) 10j = -23 + -7j + -1j + 3 + -2j Reorder the terms: 10j = -23 + 3 + -7j + -1j + -2j Combine like terms: -23 + 3 = -20 10j = -20 + -7j + -1j + -2j Combine like terms: -7j + -1j = -8j 10j = -20 + -8j + -2j Combine like terms: -8j + -2j = -10j 10j = -20 + -10j Solving 10j = -20 + -10j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '10j' to each side of the equation. 10j + 10j = -20 + -10j + 10j Combine like terms: 10j + 10j = 20j 20j = -20 + -10j + 10j Combine like terms: -10j + 10j = 0 20j = -20 + 0 20j = -20 Divide each side by '20'. j = -1 Simplifying j = -1
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