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Simplifying (7 + 5i)(4 + -9i) = 0 Multiply (7 + 5i) * (4 + -9i) (7(4 + -9i) + 5i * (4 + -9i)) = 0 ((4 * 7 + -9i * 7) + 5i * (4 + -9i)) = 0 ((28 + -63i) + 5i * (4 + -9i)) = 0 (28 + -63i + (4 * 5i + -9i * 5i)) = 0 (28 + -63i + (20i + -45i2)) = 0 Combine like terms: -63i + 20i = -43i (28 + -43i + -45i2) = 0 Solving 28 + -43i + -45i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -9i)(7 + 5i) = 0Subproblem 1
Set the factor '(4 + -9i)' equal to zero and attempt to solve: Simplifying 4 + -9i = 0 Solving 4 + -9i = 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 + -9i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9i = 0 + -4 -9i = 0 + -4 Combine like terms: 0 + -4 = -4 -9i = -4 Divide each side by '-9'. i = 0.4444444444 Simplifying i = 0.4444444444Subproblem 2
Set the factor '(7 + 5i)' equal to zero and attempt to solve: Simplifying 7 + 5i = 0 Solving 7 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5i = 0 + -7 5i = 0 + -7 Combine like terms: 0 + -7 = -7 5i = -7 Divide each side by '5'. i = -1.4 Simplifying i = -1.4Solution
i = {0.4444444444, -1.4}
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