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Simplifying (-12 + 8i)(10 + -1i) = 0 Multiply (-12 + 8i) * (10 + -1i) (-12(10 + -1i) + 8i * (10 + -1i)) = 0 ((10 * -12 + -1i * -12) + 8i * (10 + -1i)) = 0 ((-120 + 12i) + 8i * (10 + -1i)) = 0 (-120 + 12i + (10 * 8i + -1i * 8i)) = 0 (-120 + 12i + (80i + -8i2)) = 0 Combine like terms: 12i + 80i = 92i (-120 + 92i + -8i2) = 0 Solving -120 + 92i + -8i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(-30 + 23i + -2i2) = 0 Factor a trinomial. 4((-10 + i)(3 + -2i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + i)' equal to zero and attempt to solve: Simplifying -10 + i = 0 Solving -10 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + i = 0 + 10 Combine like terms: -10 + 10 = 0 0 + i = 0 + 10 i = 0 + 10 Combine like terms: 0 + 10 = 10 i = 10 Simplifying i = 10Subproblem 2
Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Solution
i = {10, 1.5}
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