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Simplifying (-16 + -27i)(-4 + 2i) = 0 Multiply (-16 + -27i) * (-4 + 2i) (-16(-4 + 2i) + -27i * (-4 + 2i)) = 0 ((-4 * -16 + 2i * -16) + -27i * (-4 + 2i)) = 0 ((64 + -32i) + -27i * (-4 + 2i)) = 0 (64 + -32i + (-4 * -27i + 2i * -27i)) = 0 (64 + -32i + (108i + -54i2)) = 0 Combine like terms: -32i + 108i = 76i (64 + 76i + -54i2) = 0 Solving 64 + 76i + -54i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(32 + 38i + -27i2) = 0 Factor a trinomial. 2((2 + -1i)(16 + 27i)) = 0 Ignore the factor 2.Subproblem 1
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 = 2Subproblem 2
Set the factor '(16 + 27i)' equal to zero and attempt to solve: Simplifying 16 + 27i = 0 Solving 16 + 27i = 0 Move all terms containing i to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + 27i = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 27i = 0 + -16 27i = 0 + -16 Combine like terms: 0 + -16 = -16 27i = -16 Divide each side by '27'. i = -0.5925925926 Simplifying i = -0.5925925926Solution
i = {2, -0.5925925926}
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