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Simplifying (5i + 2)(7i + -3) = 0 Reorder the terms: (2 + 5i)(7i + -3) = 0 Reorder the terms: (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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