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Simplifying 5(2i + 3j) + 4(3i + -3j) = 0 (2i * 5 + 3j * 5) + 4(3i + -3j) = 0 (10i + 15j) + 4(3i + -3j) = 0 10i + 15j + (3i * 4 + -3j * 4) = 0 10i + 15j + (12i + -12j) = 0 Reorder the terms: 10i + 12i + 15j + -12j = 0 Combine like terms: 10i + 12i = 22i 22i + 15j + -12j = 0 Combine like terms: 15j + -12j = 3j 22i + 3j = 0 Solving 22i + 3j = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3j' to each side of the equation. 22i + 3j + -3j = 0 + -3j Combine like terms: 3j + -3j = 0 22i + 0 = 0 + -3j 22i = 0 + -3j Remove the zero: 22i = -3j Divide each side by '22'. i = -0.1363636364j Simplifying i = -0.1363636364j
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