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Simplifying (3i)(7 + 3i) + -1(5i)(5 + 7i) = 0 Remove parenthesis around (3i) 3i(7 + 3i) + -1(5i)(5 + 7i) = 0 (7 * 3i + 3i * 3i) + -1(5i)(5 + 7i) = 0 (21i + 9i2) + -1(5i)(5 + 7i) = 0 Remove parenthesis around (5i) 21i + 9i2 + -1 * 5i(5 + 7i) = 0 Multiply -1 * 5 21i + 9i2 + -5i(5 + 7i) = 0 21i + 9i2 + (5 * -5i + 7i * -5i) = 0 21i + 9i2 + (-25i + -35i2) = 0 Reorder the terms: 21i + -25i + 9i2 + -35i2 = 0 Combine like terms: 21i + -25i = -4i -4i + 9i2 + -35i2 = 0 Combine like terms: 9i2 + -35i2 = -26i2 -4i + -26i2 = 0 Solving -4i + -26i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-2i'. -2i(2 + 13i) = 0 Ignore the factor -2.Subproblem 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 '(2 + 13i)' equal to zero and attempt to solve: Simplifying 2 + 13i = 0 Solving 2 + 13i = 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 + 13i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 13i = 0 + -2 13i = 0 + -2 Combine like terms: 0 + -2 = -2 13i = -2 Divide each side by '13'. i = -0.1538461538 Simplifying i = -0.1538461538Solution
i = {0, -0.1538461538}
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