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Simplifying (-4 + -5i)(2 + 10i) = 0 Multiply (-4 + -5i) * (2 + 10i) (-4(2 + 10i) + -5i * (2 + 10i)) = 0 ((2 * -4 + 10i * -4) + -5i * (2 + 10i)) = 0 ((-8 + -40i) + -5i * (2 + 10i)) = 0 (-8 + -40i + (2 * -5i + 10i * -5i)) = 0 (-8 + -40i + (-10i + -50i2)) = 0 Combine like terms: -40i + -10i = -50i (-8 + -50i + -50i2) = 0 Solving -8 + -50i + -50i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + 25i + 25i2) = 0 Factor a trinomial. -2((4 + 5i)(1 + 5i)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + 5i)' equal to zero and attempt to solve: Simplifying 4 + 5i = 0 Solving 4 + 5i = 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 + 5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5i = 0 + -4 5i = 0 + -4 Combine like terms: 0 + -4 = -4 5i = -4 Divide each side by '5'. i = -0.8 Simplifying i = -0.8Subproblem 2
Set the factor '(1 + 5i)' equal to zero and attempt to solve: Simplifying 1 + 5i = 0 Solving 1 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 5i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5i = 0 + -1 5i = 0 + -1 Combine like terms: 0 + -1 = -1 5i = -1 Divide each side by '5'. i = -0.2 Simplifying i = -0.2Solution
i = {-0.8, -0.2}
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