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Simplifying (5 + -10i)(3 + 5i) = 0 Multiply (5 + -10i) * (3 + 5i) (5(3 + 5i) + -10i * (3 + 5i)) = 0 ((3 * 5 + 5i * 5) + -10i * (3 + 5i)) = 0 ((15 + 25i) + -10i * (3 + 5i)) = 0 (15 + 25i + (3 * -10i + 5i * -10i)) = 0 (15 + 25i + (-30i + -50i2)) = 0 Combine like terms: 25i + -30i = -5i (15 + -5i + -50i2) = 0 Solving 15 + -5i + -50i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -1i + -10i2) = 0 Factor a trinomial. 5((1 + -2i)(3 + 5i)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -2i)' equal to zero and attempt to solve: Simplifying 1 + -2i = 0 Solving 1 + -2i = 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 + -2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2i = 0 + -1 -2i = 0 + -1 Combine like terms: 0 + -1 = -1 -2i = -1 Divide each side by '-2'. i = 0.5 Simplifying i = 0.5Subproblem 2
Set the factor '(3 + 5i)' equal to zero and attempt to solve: Simplifying 3 + 5i = 0 Solving 3 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 5i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5i = 0 + -3 5i = 0 + -3 Combine like terms: 0 + -3 = -3 5i = -3 Divide each side by '5'. i = -0.6 Simplifying i = -0.6Solution
i = {0.5, -0.6}
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