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Simplifying (4 + 7i)(9 + -1i) = 0 Multiply (4 + 7i) * (9 + -1i) (4(9 + -1i) + 7i * (9 + -1i)) = 0 ((9 * 4 + -1i * 4) + 7i * (9 + -1i)) = 0 ((36 + -4i) + 7i * (9 + -1i)) = 0 (36 + -4i + (9 * 7i + -1i * 7i)) = 0 (36 + -4i + (63i + -7i2)) = 0 Combine like terms: -4i + 63i = 59i (36 + 59i + -7i2) = 0 Solving 36 + 59i + -7i2 = 0 Solving for variable 'i'. Factor a trinomial. (9 + -1i)(4 + 7i) = 0Subproblem 1
Set the factor '(9 + -1i)' equal to zero and attempt to solve: Simplifying 9 + -1i = 0 Solving 9 + -1i = 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 + -1i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1i = 0 + -9 -1i = 0 + -9 Combine like terms: 0 + -9 = -9 -1i = -9 Divide each side by '-1'. i = 9 Simplifying i = 9Subproblem 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 = {9, -0.5714285714}
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