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Simplifying (2 + 7i)(4 + -9i) = 0 Multiply (2 + 7i) * (4 + -9i) (2(4 + -9i) + 7i * (4 + -9i)) = 0 ((4 * 2 + -9i * 2) + 7i * (4 + -9i)) = 0 ((8 + -18i) + 7i * (4 + -9i)) = 0 (8 + -18i + (4 * 7i + -9i * 7i)) = 0 (8 + -18i + (28i + -63i2)) = 0 Combine like terms: -18i + 28i = 10i (8 + 10i + -63i2) = 0 Solving 8 + 10i + -63i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -9i)(2 + 7i) = 0Subproblem 1
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 = 0.4444444444Subproblem 2
Set the factor '(2 + 7i)' equal to zero and attempt to solve: Simplifying 2 + 7i = 0 Solving 2 + 7i = 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 + 7i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7i = 0 + -2 7i = 0 + -2 Combine like terms: 0 + -2 = -2 7i = -2 Divide each side by '7'. i = -0.2857142857 Simplifying i = -0.2857142857Solution
i = {0.4444444444, -0.2857142857}
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