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Simplifying 9(2 + -1j) + 3(5 + 2j) = 2(7 + -2j) + -4(j + -1) (2 * 9 + -1j * 9) + 3(5 + 2j) = 2(7 + -2j) + -4(j + -1) (18 + -9j) + 3(5 + 2j) = 2(7 + -2j) + -4(j + -1) 18 + -9j + (5 * 3 + 2j * 3) = 2(7 + -2j) + -4(j + -1) 18 + -9j + (15 + 6j) = 2(7 + -2j) + -4(j + -1) Reorder the terms: 18 + 15 + -9j + 6j = 2(7 + -2j) + -4(j + -1) Combine like terms: 18 + 15 = 33 33 + -9j + 6j = 2(7 + -2j) + -4(j + -1) Combine like terms: -9j + 6j = -3j 33 + -3j = 2(7 + -2j) + -4(j + -1) 33 + -3j = (7 * 2 + -2j * 2) + -4(j + -1) 33 + -3j = (14 + -4j) + -4(j + -1) Reorder the terms: 33 + -3j = 14 + -4j + -4(-1 + j) 33 + -3j = 14 + -4j + (-1 * -4 + j * -4) 33 + -3j = 14 + -4j + (4 + -4j) Reorder the terms: 33 + -3j = 14 + 4 + -4j + -4j Combine like terms: 14 + 4 = 18 33 + -3j = 18 + -4j + -4j Combine like terms: -4j + -4j = -8j 33 + -3j = 18 + -8j Solving 33 + -3j = 18 + -8j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '8j' to each side of the equation. 33 + -3j + 8j = 18 + -8j + 8j Combine like terms: -3j + 8j = 5j 33 + 5j = 18 + -8j + 8j Combine like terms: -8j + 8j = 0 33 + 5j = 18 + 0 33 + 5j = 18 Add '-33' to each side of the equation. 33 + -33 + 5j = 18 + -33 Combine like terms: 33 + -33 = 0 0 + 5j = 18 + -33 5j = 18 + -33 Combine like terms: 18 + -33 = -15 5j = -15 Divide each side by '5'. j = -3 Simplifying j = -3
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