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Simplifying 0.5(5 + -7j) = 8(4j + 6) (5 * 0.5 + -7j * 0.5) = 8(4j + 6) (2.5 + -3.5j) = 8(4j + 6) Reorder the terms: 2.5 + -3.5j = 8(6 + 4j) 2.5 + -3.5j = (6 * 8 + 4j * 8) 2.5 + -3.5j = (48 + 32j) Solving 2.5 + -3.5j = 48 + 32j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-32j' to each side of the equation. 2.5 + -3.5j + -32j = 48 + 32j + -32j Combine like terms: -3.5j + -32j = -35.5j 2.5 + -35.5j = 48 + 32j + -32j Combine like terms: 32j + -32j = 0 2.5 + -35.5j = 48 + 0 2.5 + -35.5j = 48 Add '-2.5' to each side of the equation. 2.5 + -2.5 + -35.5j = 48 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -35.5j = 48 + -2.5 -35.5j = 48 + -2.5 Combine like terms: 48 + -2.5 = 45.5 -35.5j = 45.5 Divide each side by '-35.5'. j = -1.281690141 Simplifying j = -1.281690141
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