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Simplifying (-9 + 4i)(6 + -3i) = 0 Multiply (-9 + 4i) * (6 + -3i) (-9(6 + -3i) + 4i * (6 + -3i)) = 0 ((6 * -9 + -3i * -9) + 4i * (6 + -3i)) = 0 ((-54 + 27i) + 4i * (6 + -3i)) = 0 (-54 + 27i + (6 * 4i + -3i * 4i)) = 0 (-54 + 27i + (24i + -12i2)) = 0 Combine like terms: 27i + 24i = 51i (-54 + 51i + -12i2) = 0 Solving -54 + 51i + -12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(-18 + 17i + -4i2) = 0 Factor a trinomial. 3((-9 + 4i)(2 + -1i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + 4i)' equal to zero and attempt to solve: Simplifying -9 + 4i = 0 Solving -9 + 4i = 0 Move all terms containing i to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 4i = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4i = 0 + 9 4i = 0 + 9 Combine like terms: 0 + 9 = 9 4i = 9 Divide each side by '4'. i = 2.25 Simplifying i = 2.25Subproblem 2
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Solution
i = {2.25, 2}
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