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Simplifying (3 + -5i)(5 + -7i) = 0 Multiply (3 + -5i) * (5 + -7i) (3(5 + -7i) + -5i * (5 + -7i)) = 0 ((5 * 3 + -7i * 3) + -5i * (5 + -7i)) = 0 ((15 + -21i) + -5i * (5 + -7i)) = 0 (15 + -21i + (5 * -5i + -7i * -5i)) = 0 (15 + -21i + (-25i + 35i2)) = 0 Combine like terms: -21i + -25i = -46i (15 + -46i + 35i2) = 0 Solving 15 + -46i + 35i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -5i)(5 + -7i) = 0Subproblem 1
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 = 0.6Subproblem 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 = {0.6, 0.7142857143}
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