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Simplifying (4 + 5i)(3 + -7i) = 0 Multiply (4 + 5i) * (3 + -7i) (4(3 + -7i) + 5i * (3 + -7i)) = 0 ((3 * 4 + -7i * 4) + 5i * (3 + -7i)) = 0 ((12 + -28i) + 5i * (3 + -7i)) = 0 (12 + -28i + (3 * 5i + -7i * 5i)) = 0 (12 + -28i + (15i + -35i2)) = 0 Combine like terms: -28i + 15i = -13i (12 + -13i + -35i2) = 0 Solving 12 + -13i + -35i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -7i)(4 + 5i) = 0Subproblem 1
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 = 0.4285714286Subproblem 2
Set the factor '(4 + 5i)' equal to zero and attempt to solve: Simplifying 4 + 5i = 0 Solving 4 + 5i = 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 + 5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5i = 0 + -4 5i = 0 + -4 Combine like terms: 0 + -4 = -4 5i = -4 Divide each side by '5'. i = -0.8 Simplifying i = -0.8Solution
i = {0.4285714286, -0.8}
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