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Simplifying 4(3i + j)(i + 4j) = 0 Multiply (3i + j) * (i + 4j) 4(3i * (i + 4j) + j(i + 4j)) = 0 4((i * 3i + 4j * 3i) + j(i + 4j)) = 0 Reorder the terms: 4((12ij + 3i2) + j(i + 4j)) = 0 4((12ij + 3i2) + j(i + 4j)) = 0 4(12ij + 3i2 + (i * j + 4j * j)) = 0 4(12ij + 3i2 + (ij + 4j2)) = 0 Reorder the terms: 4(12ij + ij + 3i2 + 4j2) = 0 Combine like terms: 12ij + ij = 13ij 4(13ij + 3i2 + 4j2) = 0 (13ij * 4 + 3i2 * 4 + 4j2 * 4) = 0 (52ij + 12i2 + 16j2) = 0 Solving 52ij + 12i2 + 16j2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(13ij + 3i2 + 4j2) = 0 Factor a trinomial. 4((3i + j)(i + 4j)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3i + j)' equal to zero and attempt to solve: Simplifying 3i + j = 0 Solving 3i + j = 0 Move all terms containing i to the left, all other terms to the right. Add '-1j' to each side of the equation. 3i + j + -1j = 0 + -1j Combine like terms: j + -1j = 0 3i + 0 = 0 + -1j 3i = 0 + -1j Remove the zero: 3i = -1j Divide each side by '3'. i = -0.3333333333j Simplifying i = -0.3333333333jSubproblem 2
Set the factor '(i + 4j)' equal to zero and attempt to solve: Simplifying i + 4j = 0 Solving i + 4j = 0 Move all terms containing i to the left, all other terms to the right. Add '-4j' to each side of the equation. i + 4j + -4j = 0 + -4j Combine like terms: 4j + -4j = 0 i + 0 = 0 + -4j i = 0 + -4j Remove the zero: i = -4j Simplifying i = -4jSolution
i = {-0.3333333333j, -4j}
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