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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 = -43i (12 + -43i + 35i2) = 0 Solving 12 + -43i + 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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