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Simplifying (-5 + 4i)(-2 + 2i) = 0 Multiply (-5 + 4i) * (-2 + 2i) (-5(-2 + 2i) + 4i * (-2 + 2i)) = 0 ((-2 * -5 + 2i * -5) + 4i * (-2 + 2i)) = 0 ((10 + -10i) + 4i * (-2 + 2i)) = 0 (10 + -10i + (-2 * 4i + 2i * 4i)) = 0 (10 + -10i + (-8i + 8i2)) = 0 Combine like terms: -10i + -8i = -18i (10 + -18i + 8i2) = 0 Solving 10 + -18i + 8i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -9i + 4i2) = 0 Factor a trinomial. 2((1 + -1i)(5 + -4i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 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 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Subproblem 2
Set the factor '(5 + -4i)' equal to zero and attempt to solve: Simplifying 5 + -4i = 0 Solving 5 + -4i = 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 + -4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4i = 0 + -5 -4i = 0 + -5 Combine like terms: 0 + -5 = -5 -4i = -5 Divide each side by '-4'. i = 1.25 Simplifying i = 1.25Solution
i = {1, 1.25}
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