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