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Simplifying (4 + 3i)(-1 + 6i) = 0 Multiply (4 + 3i) * (-1 + 6i) (4(-1 + 6i) + 3i * (-1 + 6i)) = 0 ((-1 * 4 + 6i * 4) + 3i * (-1 + 6i)) = 0 ((-4 + 24i) + 3i * (-1 + 6i)) = 0 (-4 + 24i + (-1 * 3i + 6i * 3i)) = 0 (-4 + 24i + (-3i + 18i2)) = 0 Combine like terms: 24i + -3i = 21i (-4 + 21i + 18i2) = 0 Solving -4 + 21i + 18i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + -3i)(1 + -6i) = 0Subproblem 1
Set the factor '(-4 + -3i)' equal to zero and attempt to solve: Simplifying -4 + -3i = 0 Solving -4 + -3i = 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 + -3i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3i = 0 + 4 -3i = 0 + 4 Combine like terms: 0 + 4 = 4 -3i = 4 Divide each side by '-3'. i = -1.333333333 Simplifying i = -1.333333333Subproblem 2
Set the factor '(1 + -6i)' equal to zero and attempt to solve: Simplifying 1 + -6i = 0 Solving 1 + -6i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -6i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6i = 0 + -1 -6i = 0 + -1 Combine like terms: 0 + -1 = -1 -6i = -1 Divide each side by '-6'. i = 0.1666666667 Simplifying i = 0.1666666667Solution
i = {-1.333333333, 0.1666666667}
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