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Simplifying (7 + i)(5 + -9i) = 0 Multiply (7 + i) * (5 + -9i) (7(5 + -9i) + i(5 + -9i)) = 0 ((5 * 7 + -9i * 7) + i(5 + -9i)) = 0 ((35 + -63i) + i(5 + -9i)) = 0 (35 + -63i + (5 * i + -9i * i)) = 0 (35 + -63i + (5i + -9i2)) = 0 Combine like terms: -63i + 5i = -58i (35 + -58i + -9i2) = 0 Solving 35 + -58i + -9i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -9i)(7 + i) = 0Subproblem 1
Set the factor '(5 + -9i)' equal to zero and attempt to solve: Simplifying 5 + -9i = 0 Solving 5 + -9i = 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 + -9i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9i = 0 + -5 -9i = 0 + -5 Combine like terms: 0 + -5 = -5 -9i = -5 Divide each side by '-9'. i = 0.5555555556 Simplifying i = 0.5555555556Subproblem 2
Set the factor '(7 + i)' equal to zero and attempt to solve: Simplifying 7 + i = 0 Solving 7 + i = 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 + i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + i = 0 + -7 i = 0 + -7 Combine like terms: 0 + -7 = -7 i = -7 Simplifying i = -7Solution
i = {0.5555555556, -7}
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