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Simplifying (4 + 7i)(5 + 2i) = 0 Multiply (4 + 7i) * (5 + 2i) (4(5 + 2i) + 7i * (5 + 2i)) = 0 ((5 * 4 + 2i * 4) + 7i * (5 + 2i)) = 0 ((20 + 8i) + 7i * (5 + 2i)) = 0 (20 + 8i + (5 * 7i + 2i * 7i)) = 0 (20 + 8i + (35i + 14i2)) = 0 Combine like terms: 8i + 35i = 43i (20 + 43i + 14i2) = 0 Solving 20 + 43i + 14i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + 2i)(4 + 7i) = 0Subproblem 1
Set the factor '(5 + 2i)' equal to zero and attempt to solve: Simplifying 5 + 2i = 0 Solving 5 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2i = 0 + -5 2i = 0 + -5 Combine like terms: 0 + -5 = -5 2i = -5 Divide each side by '2'. i = -2.5 Simplifying i = -2.5Subproblem 2
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 = -0.5714285714Solution
i = {-2.5, -0.5714285714}
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