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Simplifying (3 + 7i)(5 + -9i) = 0 Multiply (3 + 7i) * (5 + -9i) (3(5 + -9i) + 7i * (5 + -9i)) = 0 ((5 * 3 + -9i * 3) + 7i * (5 + -9i)) = 0 ((15 + -27i) + 7i * (5 + -9i)) = 0 (15 + -27i + (5 * 7i + -9i * 7i)) = 0 (15 + -27i + (35i + -63i2)) = 0 Combine like terms: -27i + 35i = 8i (15 + 8i + -63i2) = 0 Solving 15 + 8i + -63i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -9i)(3 + 7i) = 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 '(3 + 7i)' equal to zero and attempt to solve: Simplifying 3 + 7i = 0 Solving 3 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 7i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7i = 0 + -3 7i = 0 + -3 Combine like terms: 0 + -3 = -3 7i = -3 Divide each side by '7'. i = -0.4285714286 Simplifying i = -0.4285714286Solution
i = {0.5555555556, -0.4285714286}
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