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Simplifying (-4 + -10i)(-1 + 9i) = 0 Multiply (-4 + -10i) * (-1 + 9i) (-4(-1 + 9i) + -10i * (-1 + 9i)) = 0 ((-1 * -4 + 9i * -4) + -10i * (-1 + 9i)) = 0 ((4 + -36i) + -10i * (-1 + 9i)) = 0 (4 + -36i + (-1 * -10i + 9i * -10i)) = 0 (4 + -36i + (10i + -90i2)) = 0 Combine like terms: -36i + 10i = -26i (4 + -26i + -90i2) = 0 Solving 4 + -26i + -90i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -13i + -45i2) = 0 Factor a trinomial. 2((1 + -9i)(2 + 5i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -9i)' equal to zero and attempt to solve: Simplifying 1 + -9i = 0 Solving 1 + -9i = 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 + -9i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9i = 0 + -1 -9i = 0 + -1 Combine like terms: 0 + -1 = -1 -9i = -1 Divide each side by '-9'. i = 0.1111111111 Simplifying i = 0.1111111111Subproblem 2
Set the factor '(2 + 5i)' equal to zero and attempt to solve: Simplifying 2 + 5i = 0 Solving 2 + 5i = 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 + 5i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5i = 0 + -2 5i = 0 + -2 Combine like terms: 0 + -2 = -2 5i = -2 Divide each side by '5'. i = -0.4 Simplifying i = -0.4Solution
i = {0.1111111111, -0.4}
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