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Simplifying (9 + -2i)(4 + 7i) = 0 Multiply (9 + -2i) * (4 + 7i) (9(4 + 7i) + -2i * (4 + 7i)) = 0 ((4 * 9 + 7i * 9) + -2i * (4 + 7i)) = 0 ((36 + 63i) + -2i * (4 + 7i)) = 0 (36 + 63i + (4 * -2i + 7i * -2i)) = 0 (36 + 63i + (-8i + -14i2)) = 0 Combine like terms: 63i + -8i = 55i (36 + 55i + -14i2) = 0 Solving 36 + 55i + -14i2 = 0 Solving for variable 'i'. Factor a trinomial. (9 + -2i)(4 + 7i) = 0Subproblem 1
Set the factor '(9 + -2i)' equal to zero and attempt to solve: Simplifying 9 + -2i = 0 Solving 9 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2i = 0 + -9 -2i = 0 + -9 Combine like terms: 0 + -9 = -9 -2i = -9 Divide each side by '-2'. i = 4.5 Simplifying i = 4.5Subproblem 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 = {4.5, -0.5714285714}
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