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Simplifying (7 + -9i)(9 + 4i) = 0 Multiply (7 + -9i) * (9 + 4i) (7(9 + 4i) + -9i * (9 + 4i)) = 0 ((9 * 7 + 4i * 7) + -9i * (9 + 4i)) = 0 ((63 + 28i) + -9i * (9 + 4i)) = 0 (63 + 28i + (9 * -9i + 4i * -9i)) = 0 (63 + 28i + (-81i + -36i2)) = 0 Combine like terms: 28i + -81i = -53i (63 + -53i + -36i2) = 0 Solving 63 + -53i + -36i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -9i)(9 + 4i) = 0Subproblem 1
Set the factor '(7 + -9i)' equal to zero and attempt to solve: Simplifying 7 + -9i = 0 Solving 7 + -9i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -9i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9i = 0 + -7 -9i = 0 + -7 Combine like terms: 0 + -7 = -7 -9i = -7 Divide each side by '-9'. i = 0.7777777778 Simplifying i = 0.7777777778Subproblem 2
Set the factor '(9 + 4i)' equal to zero and attempt to solve: Simplifying 9 + 4i = 0 Solving 9 + 4i = 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 + 4i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4i = 0 + -9 4i = 0 + -9 Combine like terms: 0 + -9 = -9 4i = -9 Divide each side by '4'. i = -2.25 Simplifying i = -2.25Solution
i = {0.7777777778, -2.25}
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