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Simplifying (3 + i)(5 + -2i) = 0 Multiply (3 + i) * (5 + -2i) (3(5 + -2i) + i(5 + -2i)) = 0 ((5 * 3 + -2i * 3) + i(5 + -2i)) = 0 ((15 + -6i) + i(5 + -2i)) = 0 (15 + -6i + (5 * i + -2i * i)) = 0 (15 + -6i + (5i + -2i2)) = 0 Combine like terms: -6i + 5i = -1i (15 + -1i + -2i2) = 0 Solving 15 + -1i + -2i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -2i)(3 + i) = 0Subproblem 1
Set the factor '(5 + -2i)' equal to zero and attempt to solve: Simplifying 5 + -2i = 0 Solving 5 + -2i = 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 + -2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2i = 0 + -5 -2i = 0 + -5 Combine like terms: 0 + -5 = -5 -2i = -5 Divide each side by '-2'. i = 2.5 Simplifying i = 2.5Subproblem 2
Set the factor '(3 + i)' equal to zero and attempt to solve: Simplifying 3 + i = 0 Solving 3 + i = 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 + i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + i = 0 + -3 i = 0 + -3 Combine like terms: 0 + -3 = -3 i = -3 Simplifying i = -3Solution
i = {2.5, -3}
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