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Simplifying (-2 + 3i)(-3 + 10i) = 0 Multiply (-2 + 3i) * (-3 + 10i) (-2(-3 + 10i) + 3i * (-3 + 10i)) = 0 ((-3 * -2 + 10i * -2) + 3i * (-3 + 10i)) = 0 ((6 + -20i) + 3i * (-3 + 10i)) = 0 (6 + -20i + (-3 * 3i + 10i * 3i)) = 0 (6 + -20i + (-9i + 30i2)) = 0 Combine like terms: -20i + -9i = -29i (6 + -29i + 30i2) = 0 Solving 6 + -29i + 30i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -10i)(2 + -3i) = 0Subproblem 1
Set the factor '(3 + -10i)' equal to zero and attempt to solve: Simplifying 3 + -10i = 0 Solving 3 + -10i = 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 + -10i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10i = 0 + -3 -10i = 0 + -3 Combine like terms: 0 + -3 = -3 -10i = -3 Divide each side by '-10'. i = 0.3 Simplifying i = 0.3Subproblem 2
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 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 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Solution
i = {0.3, 0.6666666667}
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