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Simplifying (5 + -3i)(5 + -3i) = 0 Multiply (5 + -3i) * (5 + -3i) (5(5 + -3i) + -3i * (5 + -3i)) = 0 ((5 * 5 + -3i * 5) + -3i * (5 + -3i)) = 0 ((25 + -15i) + -3i * (5 + -3i)) = 0 (25 + -15i + (5 * -3i + -3i * -3i)) = 0 (25 + -15i + (-15i + 9i2)) = 0 Combine like terms: -15i + -15i = -30i (25 + -30i + 9i2) = 0 Solving 25 + -30i + 9i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -3i)(5 + -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 '(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 = 1.666666667Solution
i = {1.666666667, 1.666666667}
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