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Simplifying (3 + 5i)(8 + 7i) = 0 Multiply (3 + 5i) * (8 + 7i) (3(8 + 7i) + 5i * (8 + 7i)) = 0 ((8 * 3 + 7i * 3) + 5i * (8 + 7i)) = 0 ((24 + 21i) + 5i * (8 + 7i)) = 0 (24 + 21i + (8 * 5i + 7i * 5i)) = 0 (24 + 21i + (40i + 35i2)) = 0 Combine like terms: 21i + 40i = 61i (24 + 61i + 35i2) = 0 Solving 24 + 61i + 35i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + 7i)(3 + 5i) = 0Subproblem 1
Set the factor '(8 + 7i)' equal to zero and attempt to solve: Simplifying 8 + 7i = 0 Solving 8 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 7i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7i = 0 + -8 7i = 0 + -8 Combine like terms: 0 + -8 = -8 7i = -8 Divide each side by '7'. i = -1.142857143 Simplifying i = -1.142857143Subproblem 2
Set the factor '(3 + 5i)' equal to zero and attempt to solve: Simplifying 3 + 5i = 0 Solving 3 + 5i = 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 + 5i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5i = 0 + -3 5i = 0 + -3 Combine like terms: 0 + -3 = -3 5i = -3 Divide each side by '5'. i = -0.6 Simplifying i = -0.6Solution
i = {-1.142857143, -0.6}
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