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Simplifying (4 + 3i)(5 + 5i) = 0 Multiply (4 + 3i) * (5 + 5i) (4(5 + 5i) + 3i * (5 + 5i)) = 0 ((5 * 4 + 5i * 4) + 3i * (5 + 5i)) = 0 ((20 + 20i) + 3i * (5 + 5i)) = 0 (20 + 20i + (5 * 3i + 5i * 3i)) = 0 (20 + 20i + (15i + 15i2)) = 0 Combine like terms: 20i + 15i = 35i (20 + 35i + 15i2) = 0 Solving 20 + 35i + 15i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '5'. 5(4 + 7i + 3i2) = 0 Factor a trinomial. 5((4 + 3i)(1 + i)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + 3i)' equal to zero and attempt to solve: Simplifying 4 + 3i = 0 Solving 4 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3i = 0 + -4 3i = 0 + -4 Combine like terms: 0 + -4 = -4 3i = -4 Divide each side by '3'. i = -1.333333333 Simplifying i = -1.333333333Subproblem 2
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {-1.333333333, -1}
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