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Simplifying -4k(2i + 3) + -6ki + 8k = 0 Reorder the terms: -4k(3 + 2i) + -6ki + 8k = 0 (3 * -4k + 2i * -4k) + -6ki + 8k = 0 Reorder the terms: (-8ik + -12k) + -6ki + 8k = 0 (-8ik + -12k) + -6ki + 8k = 0 Reorder the terms: -8ik + -6ik + -12k + 8k = 0 Combine like terms: -8ik + -6ik = -14ik -14ik + -12k + 8k = 0 Combine like terms: -12k + 8k = -4k -14ik + -4k = 0 Solving -14ik + -4k = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '4k' to each side of the equation. -14ik + -4k + 4k = 0 + 4k Combine like terms: -4k + 4k = 0 -14ik + 0 = 0 + 4k -14ik = 0 + 4k Remove the zero: -14ik = 4k Divide each side by '-14k'. i = -0.2857142857 Simplifying i = -0.2857142857
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