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Simplifying (2 + -5i)(3 + 7i) = 0 Multiply (2 + -5i) * (3 + 7i) (2(3 + 7i) + -5i * (3 + 7i)) = 0 ((3 * 2 + 7i * 2) + -5i * (3 + 7i)) = 0 ((6 + 14i) + -5i * (3 + 7i)) = 0 (6 + 14i + (3 * -5i + 7i * -5i)) = 0 (6 + 14i + (-15i + -35i2)) = 0 Combine like terms: 14i + -15i = -1i (6 + -1i + -35i2) = 0 Solving 6 + -1i + -35i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -5i)(3 + 7i) = 0Subproblem 1
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 = 0.4Subproblem 2
Set the factor '(3 + 7i)' equal to zero and attempt to solve: Simplifying 3 + 7i = 0 Solving 3 + 7i = 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 + 7i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7i = 0 + -3 7i = 0 + -3 Combine like terms: 0 + -3 = -3 7i = -3 Divide each side by '7'. i = -0.4285714286 Simplifying i = -0.4285714286Solution
i = {0.4, -0.4285714286}
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