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Simplifying i(7 + 9i)(7 + -9i) = 0 Multiply (7 + 9i) * (7 + -9i) i(7(7 + -9i) + 9i * (7 + -9i)) = 0 i((7 * 7 + -9i * 7) + 9i * (7 + -9i)) = 0 i((49 + -63i) + 9i * (7 + -9i)) = 0 i(49 + -63i + (7 * 9i + -9i * 9i)) = 0 i(49 + -63i + (63i + -81i2)) = 0 Combine like terms: -63i + 63i = 0 i(49 + 0 + -81i2) = 0 i(49 + -81i2) = 0 (49 * i + -81i2 * i) = 0 (49i + -81i3) = 0 Solving 49i + -81i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), 'i'. i(49 + -81i2) = 0 Factor a difference between two squares. i((7 + 9i)(7 + -9i)) = 0Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 2
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 3
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 = 0.7777777778Solution
i = {0, -0.7777777778, 0.7777777778}
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