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Simplifying (4 + -9i)(9 + i) = 0 Multiply (4 + -9i) * (9 + i) (4(9 + i) + -9i * (9 + i)) = 0 ((9 * 4 + i * 4) + -9i * (9 + i)) = 0 ((36 + 4i) + -9i * (9 + i)) = 0 (36 + 4i + (9 * -9i + i * -9i)) = 0 (36 + 4i + (-81i + -9i2)) = 0 Combine like terms: 4i + -81i = -77i (36 + -77i + -9i2) = 0 Solving 36 + -77i + -9i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -9i)(9 + i) = 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 '(9 + i)' equal to zero and attempt to solve: Simplifying 9 + i = 0 Solving 9 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + i = 0 + -9 i = 0 + -9 Combine like terms: 0 + -9 = -9 i = -9 Simplifying i = -9Solution
i = {0.4444444444, -9}
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