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Simplifying 4(-4 + k) + 8(6 + 3j) = 0 (-4 * 4 + k * 4) + 8(6 + 3j) = 0 (-16 + 4k) + 8(6 + 3j) = 0 -16 + 4k + (6 * 8 + 3j * 8) = 0 -16 + 4k + (48 + 24j) = 0 Reorder the terms: -16 + 48 + 24j + 4k = 0 Combine like terms: -16 + 48 = 32 32 + 24j + 4k = 0 Solving 32 + 24j + 4k = 0 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + 24j + -32 + 4k = 0 + -32 Reorder the terms: 32 + -32 + 24j + 4k = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 24j + 4k = 0 + -32 24j + 4k = 0 + -32 Combine like terms: 0 + -32 = -32 24j + 4k = -32 Add '-4k' to each side of the equation. 24j + 4k + -4k = -32 + -4k Combine like terms: 4k + -4k = 0 24j + 0 = -32 + -4k 24j = -32 + -4k Divide each side by '24'. j = -1.333333333 + -0.1666666667k Simplifying j = -1.333333333 + -0.1666666667k
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