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Simplifying -5(1 + -5j) + 5(-8j + -2) = -4j + -8j (1 * -5 + -5j * -5) + 5(-8j + -2) = -4j + -8j (-5 + 25j) + 5(-8j + -2) = -4j + -8j Reorder the terms: -5 + 25j + 5(-2 + -8j) = -4j + -8j -5 + 25j + (-2 * 5 + -8j * 5) = -4j + -8j -5 + 25j + (-10 + -40j) = -4j + -8j Reorder the terms: -5 + -10 + 25j + -40j = -4j + -8j Combine like terms: -5 + -10 = -15 -15 + 25j + -40j = -4j + -8j Combine like terms: 25j + -40j = -15j -15 + -15j = -4j + -8j Combine like terms: -4j + -8j = -12j -15 + -15j = -12j Solving -15 + -15j = -12j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '12j' to each side of the equation. -15 + -15j + 12j = -12j + 12j Combine like terms: -15j + 12j = -3j -15 + -3j = -12j + 12j Combine like terms: -12j + 12j = 0 -15 + -3j = 0 Add '15' to each side of the equation. -15 + 15 + -3j = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -3j = 0 + 15 -3j = 0 + 15 Combine like terms: 0 + 15 = 15 -3j = 15 Divide each side by '-3'. j = -5 Simplifying j = -5
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