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Simplifying 6(3h + 4i) + -7(2h + -1i) = 0 (3h * 6 + 4i * 6) + -7(2h + -1i) = 0 (18h + 24i) + -7(2h + -1i) = 0 18h + 24i + (2h * -7 + -1i * -7) = 0 18h + 24i + (-14h + 7i) = 0 Reorder the terms: 18h + -14h + 24i + 7i = 0 Combine like terms: 18h + -14h = 4h 4h + 24i + 7i = 0 Combine like terms: 24i + 7i = 31i 4h + 31i = 0 Solving 4h + 31i = 0 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-31i' to each side of the equation. 4h + 31i + -31i = 0 + -31i Combine like terms: 31i + -31i = 0 4h + 0 = 0 + -31i 4h = 0 + -31i Remove the zero: 4h = -31i Divide each side by '4'. h = -7.75i Simplifying h = -7.75i
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