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Simplifying (3 + -2i)(5 + i)(4 + -2i) = 0 Multiply (3 + -2i) * (5 + i) (3(5 + i) + -2i * (5 + i))(4 + -2i) = 0 ((5 * 3 + i * 3) + -2i * (5 + i))(4 + -2i) = 0 ((15 + 3i) + -2i * (5 + i))(4 + -2i) = 0 (15 + 3i + (5 * -2i + i * -2i))(4 + -2i) = 0 (15 + 3i + (-10i + -2i2))(4 + -2i) = 0 Combine like terms: 3i + -10i = -7i (15 + -7i + -2i2)(4 + -2i) = 0 Multiply (15 + -7i + -2i2) * (4 + -2i) (15(4 + -2i) + -7i * (4 + -2i) + -2i2 * (4 + -2i)) = 0 ((4 * 15 + -2i * 15) + -7i * (4 + -2i) + -2i2 * (4 + -2i)) = 0 ((60 + -30i) + -7i * (4 + -2i) + -2i2 * (4 + -2i)) = 0 (60 + -30i + (4 * -7i + -2i * -7i) + -2i2 * (4 + -2i)) = 0 (60 + -30i + (-28i + 14i2) + -2i2 * (4 + -2i)) = 0 (60 + -30i + -28i + 14i2 + (4 * -2i2 + -2i * -2i2)) = 0 (60 + -30i + -28i + 14i2 + (-8i2 + 4i3)) = 0 Combine like terms: -30i + -28i = -58i (60 + -58i + 14i2 + -8i2 + 4i3) = 0 Combine like terms: 14i2 + -8i2 = 6i2 (60 + -58i + 6i2 + 4i3) = 0 Solving 60 + -58i + 6i2 + 4i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(30 + -29i + 3i2 + 2i3) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + -29i + 3i2 + 2i3)' equal to zero and attempt to solve: Simplifying 30 + -29i + 3i2 + 2i3 = 0 Solving 30 + -29i + 3i2 + 2i3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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