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Simplifying (7 + -3i)(-5 + -3i) = 0 Multiply (7 + -3i) * (-5 + -3i) (7(-5 + -3i) + -3i * (-5 + -3i)) = 0 ((-5 * 7 + -3i * 7) + -3i * (-5 + -3i)) = 0 ((-35 + -21i) + -3i * (-5 + -3i)) = 0 (-35 + -21i + (-5 * -3i + -3i * -3i)) = 0 (-35 + -21i + (15i + 9i2)) = 0 Combine like terms: -21i + 15i = -6i (-35 + -6i + 9i2) = 0 Solving -35 + -6i + 9i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + -3i)(7 + -3i) = 0Subproblem 1
Set the factor '(-5 + -3i)' equal to zero and attempt to solve: Simplifying -5 + -3i = 0 Solving -5 + -3i = 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 + -3i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3i = 0 + 5 -3i = 0 + 5 Combine like terms: 0 + 5 = 5 -3i = 5 Divide each side by '-3'. i = -1.666666667 Simplifying i = -1.666666667Subproblem 2
Set the factor '(7 + -3i)' equal to zero and attempt to solve: Simplifying 7 + -3i = 0 Solving 7 + -3i = 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 + -3i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3i = 0 + -7 -3i = 0 + -7 Combine like terms: 0 + -7 = -7 -3i = -7 Divide each side by '-3'. i = 2.333333333 Simplifying i = 2.333333333Solution
i = {-1.666666667, 2.333333333}
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