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Simplifying (7 + 9i)(1 + 5i) = 0 Multiply (7 + 9i) * (1 + 5i) (7(1 + 5i) + 9i * (1 + 5i)) = 0 ((1 * 7 + 5i * 7) + 9i * (1 + 5i)) = 0 ((7 + 35i) + 9i * (1 + 5i)) = 0 (7 + 35i + (1 * 9i + 5i * 9i)) = 0 (7 + 35i + (9i + 45i2)) = 0 Combine like terms: 35i + 9i = 44i (7 + 44i + 45i2) = 0 Solving 7 + 44i + 45i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + 9i)(1 + 5i) = 0Subproblem 1
Set the factor '(7 + 9i)' equal to zero and attempt to solve: Simplifying 7 + 9i = 0 Solving 7 + 9i = 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 + 9i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9i = 0 + -7 9i = 0 + -7 Combine like terms: 0 + -7 = -7 9i = -7 Divide each side by '9'. i = -0.7777777778 Simplifying i = -0.7777777778Subproblem 2
Set the factor '(1 + 5i)' equal to zero and attempt to solve: Simplifying 1 + 5i = 0 Solving 1 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 5i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5i = 0 + -1 5i = 0 + -1 Combine like terms: 0 + -1 = -1 5i = -1 Divide each side by '5'. i = -0.2 Simplifying i = -0.2Solution
i = {-0.7777777778, -0.2}
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