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Simplifying (-4 + -9i)(8 + 2i) = 0 Multiply (-4 + -9i) * (8 + 2i) (-4(8 + 2i) + -9i * (8 + 2i)) = 0 ((8 * -4 + 2i * -4) + -9i * (8 + 2i)) = 0 ((-32 + -8i) + -9i * (8 + 2i)) = 0 (-32 + -8i + (8 * -9i + 2i * -9i)) = 0 (-32 + -8i + (-72i + -18i2)) = 0 Combine like terms: -8i + -72i = -80i (-32 + -80i + -18i2) = 0 Solving -32 + -80i + -18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-2'. -2(16 + 40i + 9i2) = 0 Factor a trinomial. -2((4 + i)(4 + 9i)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + i)' equal to zero and attempt to solve: Simplifying 4 + i = 0 Solving 4 + i = 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 + i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + i = 0 + -4 i = 0 + -4 Combine like terms: 0 + -4 = -4 i = -4 Simplifying i = -4Subproblem 2
Set the factor '(4 + 9i)' equal to zero and attempt to solve: Simplifying 4 + 9i = 0 Solving 4 + 9i = 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 + 9i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 9i = 0 + -4 9i = 0 + -4 Combine like terms: 0 + -4 = -4 9i = -4 Divide each side by '9'. i = -0.4444444444 Simplifying i = -0.4444444444Solution
i = {-4, -0.4444444444}
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