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Simplifying (-2 + 5i)(1 + 3i) = 0 Multiply (-2 + 5i) * (1 + 3i) (-2(1 + 3i) + 5i * (1 + 3i)) = 0 ((1 * -2 + 3i * -2) + 5i * (1 + 3i)) = 0 ((-2 + -6i) + 5i * (1 + 3i)) = 0 (-2 + -6i + (1 * 5i + 3i * 5i)) = 0 (-2 + -6i + (5i + 15i2)) = 0 Combine like terms: -6i + 5i = -1i (-2 + -1i + 15i2) = 0 Solving -2 + -1i + 15i2 = 0 Solving for variable 'i'. Factor a trinomial. (-1 + -3i)(2 + -5i) = 0Subproblem 1
Set the factor '(-1 + -3i)' equal to zero and attempt to solve: Simplifying -1 + -3i = 0 Solving -1 + -3i = 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 + -3i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3i = 0 + 1 -3i = 0 + 1 Combine like terms: 0 + 1 = 1 -3i = 1 Divide each side by '-3'. i = -0.3333333333 Simplifying i = -0.3333333333Subproblem 2
Set the factor '(2 + -5i)' equal to zero and attempt to solve: Simplifying 2 + -5i = 0 Solving 2 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5i = 0 + -2 -5i = 0 + -2 Combine like terms: 0 + -2 = -2 -5i = -2 Divide each side by '-5'. i = 0.4 Simplifying i = 0.4Solution
i = {-0.3333333333, 0.4}
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