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Simplifying (-4 + 2i)(-4 + i) = 0 Multiply (-4 + 2i) * (-4 + i) (-4(-4 + i) + 2i * (-4 + i)) = 0 ((-4 * -4 + i * -4) + 2i * (-4 + i)) = 0 ((16 + -4i) + 2i * (-4 + i)) = 0 (16 + -4i + (-4 * 2i + i * 2i)) = 0 (16 + -4i + (-8i + 2i2)) = 0 Combine like terms: -4i + -8i = -12i (16 + -12i + 2i2) = 0 Solving 16 + -12i + 2i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -6i + i2) = 0 Factor a trinomial. 2((2 + -1i)(4 + -1i)) = 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 '(4 + -1i)' equal to zero and attempt to solve: Simplifying 4 + -1i = 0 Solving 4 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i = 0 + -4 -1i = 0 + -4 Combine like terms: 0 + -4 = -4 -1i = -4 Divide each side by '-1'. i = 4 Simplifying i = 4Solution
i = {2, 4}
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