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Simplifying (-3 + 10i)(-4 + -9i) = 0 Multiply (-3 + 10i) * (-4 + -9i) (-3(-4 + -9i) + 10i * (-4 + -9i)) = 0 ((-4 * -3 + -9i * -3) + 10i * (-4 + -9i)) = 0 ((12 + 27i) + 10i * (-4 + -9i)) = 0 (12 + 27i + (-4 * 10i + -9i * 10i)) = 0 (12 + 27i + (-40i + -90i2)) = 0 Combine like terms: 27i + -40i = -13i (12 + -13i + -90i2) = 0 Solving 12 + -13i + -90i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -10i)(4 + 9i) = 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 '(4 + 9i)' equal to zero and attempt to solve: Simplifying 4 + 9i = 0 Solving 4 + 9i = 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 + 9i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 9i = 0 + -4 9i = 0 + -4 Combine like terms: 0 + -4 = -4 9i = -4 Divide each side by '9'. i = -0.4444444444 Simplifying i = -0.4444444444Solution
i = {0.3, -0.4444444444}
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