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Simplifying 4(h + i) + -1(2h + 3i) = 0 (h * 4 + i * 4) + -1(2h + 3i) = 0 (4h + 4i) + -1(2h + 3i) = 0 4h + 4i + (2h * -1 + 3i * -1) = 0 4h + 4i + (-2h + -3i) = 0 Reorder the terms: 4h + -2h + 4i + -3i = 0 Combine like terms: 4h + -2h = 2h 2h + 4i + -3i = 0 Combine like terms: 4i + -3i = 1i 2h + 1i = 0 Solving 2h + 1i = 0 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1i' to each side of the equation. 2h + 1i + -1i = 0 + -1i Combine like terms: 1i + -1i = 0 2h + 0 = 0 + -1i 2h = 0 + -1i Remove the zero: 2h = -1i Divide each side by '2'. h = -0.5i Simplifying h = -0.5i
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