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Simplifying (2 + 5i)(-4 + -7i) = 0 Multiply (2 + 5i) * (-4 + -7i) (2(-4 + -7i) + 5i * (-4 + -7i)) = 0 ((-4 * 2 + -7i * 2) + 5i * (-4 + -7i)) = 0 ((-8 + -14i) + 5i * (-4 + -7i)) = 0 (-8 + -14i + (-4 * 5i + -7i * 5i)) = 0 (-8 + -14i + (-20i + -35i2)) = 0 Combine like terms: -14i + -20i = -34i (-8 + -34i + -35i2) = 0 Solving -8 + -34i + -35i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 34i + 35i2) = 0 Factor a trinomial. -1((4 + 7i)(2 + 5i)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 7i)' equal to zero and attempt to solve: Simplifying 4 + 7i = 0 Solving 4 + 7i = 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 + 7i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7i = 0 + -4 7i = 0 + -4 Combine like terms: 0 + -4 = -4 7i = -4 Divide each side by '7'. i = -0.5714285714 Simplifying i = -0.5714285714Subproblem 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 = {-0.5714285714, -0.4}
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