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Simplifying (2 + 7i)(3 + -5i) = 0 Multiply (2 + 7i) * (3 + -5i) (2(3 + -5i) + 7i * (3 + -5i)) = 0 ((3 * 2 + -5i * 2) + 7i * (3 + -5i)) = 0 ((6 + -10i) + 7i * (3 + -5i)) = 0 (6 + -10i + (3 * 7i + -5i * 7i)) = 0 (6 + -10i + (21i + -35i2)) = 0 Combine like terms: -10i + 21i = 11i (6 + 11i + -35i2) = 0 Solving 6 + 11i + -35i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -5i)(2 + 7i) = 0Subproblem 1
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 = 0.6Subproblem 2
Set the factor '(2 + 7i)' equal to zero and attempt to solve: Simplifying 2 + 7i = 0 Solving 2 + 7i = 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 + 7i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7i = 0 + -2 7i = 0 + -2 Combine like terms: 0 + -2 = -2 7i = -2 Divide each side by '7'. i = -0.2857142857 Simplifying i = -0.2857142857Solution
i = {0.6, -0.2857142857}
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