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Simplifying 9(z + -1j) + 3(5 + 2j) = (7 + -2j) + -4 Reorder the terms: 9(-1j + z) + 3(5 + 2j) = (7 + -2j) + -4 (-1j * 9 + z * 9) + 3(5 + 2j) = (7 + -2j) + -4 (-9j + 9z) + 3(5 + 2j) = (7 + -2j) + -4 -9j + 9z + (5 * 3 + 2j * 3) = (7 + -2j) + -4 -9j + 9z + (15 + 6j) = (7 + -2j) + -4 Reorder the terms: 15 + -9j + 6j + 9z = (7 + -2j) + -4 Combine like terms: -9j + 6j = -3j 15 + -3j + 9z = (7 + -2j) + -4 Remove parenthesis around (7 + -2j) 15 + -3j + 9z = 7 + -2j + -4 Reorder the terms: 15 + -3j + 9z = 7 + -4 + -2j Combine like terms: 7 + -4 = 3 15 + -3j + 9z = 3 + -2j Solving 15 + -3j + 9z = 3 + -2j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '2j' to each side of the equation. 15 + -3j + 2j + 9z = 3 + -2j + 2j Combine like terms: -3j + 2j = -1j 15 + -1j + 9z = 3 + -2j + 2j Combine like terms: -2j + 2j = 0 15 + -1j + 9z = 3 + 0 15 + -1j + 9z = 3 Add '-15' to each side of the equation. 15 + -1j + -15 + 9z = 3 + -15 Reorder the terms: 15 + -15 + -1j + 9z = 3 + -15 Combine like terms: 15 + -15 = 0 0 + -1j + 9z = 3 + -15 -1j + 9z = 3 + -15 Combine like terms: 3 + -15 = -12 -1j + 9z = -12 Add '-9z' to each side of the equation. -1j + 9z + -9z = -12 + -9z Combine like terms: 9z + -9z = 0 -1j + 0 = -12 + -9z -1j = -12 + -9z Divide each side by '-1'. j = 12 + 9z Simplifying j = 12 + 9z
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