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Simplifying 4(2i + j) + 3(i + -1j) = 0 (2i * 4 + j * 4) + 3(i + -1j) = 0 (8i + 4j) + 3(i + -1j) = 0 8i + 4j + (i * 3 + -1j * 3) = 0 8i + 4j + (3i + -3j) = 0 Reorder the terms: 8i + 3i + 4j + -3j = 0 Combine like terms: 8i + 3i = 11i 11i + 4j + -3j = 0 Combine like terms: 4j + -3j = 1j 11i + 1j = 0 Solving 11i + 1j = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1j' to each side of the equation. 11i + 1j + -1j = 0 + -1j Combine like terms: 1j + -1j = 0 11i + 0 = 0 + -1j 11i = 0 + -1j Remove the zero: 11i = -1j Divide each side by '11'. i = -0.09090909091j Simplifying i = -0.09090909091j
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