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Simplifying (5 + -7i)(3 + -8i) = 0 Multiply (5 + -7i) * (3 + -8i) (5(3 + -8i) + -7i * (3 + -8i)) = 0 ((3 * 5 + -8i * 5) + -7i * (3 + -8i)) = 0 ((15 + -40i) + -7i * (3 + -8i)) = 0 (15 + -40i + (3 * -7i + -8i * -7i)) = 0 (15 + -40i + (-21i + 56i2)) = 0 Combine like terms: -40i + -21i = -61i (15 + -61i + 56i2) = 0 Solving 15 + -61i + 56i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -8i)(5 + -7i) = 0Subproblem 1
Set the factor '(3 + -8i)' equal to zero and attempt to solve: Simplifying 3 + -8i = 0 Solving 3 + -8i = 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 + -8i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8i = 0 + -3 -8i = 0 + -3 Combine like terms: 0 + -3 = -3 -8i = -3 Divide each side by '-8'. i = 0.375 Simplifying i = 0.375Subproblem 2
Set the factor '(5 + -7i)' equal to zero and attempt to solve: Simplifying 5 + -7i = 0 Solving 5 + -7i = 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 + -7i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7i = 0 + -5 -7i = 0 + -5 Combine like terms: 0 + -5 = -5 -7i = -5 Divide each side by '-7'. i = 0.7142857143 Simplifying i = 0.7142857143Solution
i = {0.375, 0.7142857143}
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