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Simplifying (5 + 6i)(-4 + 7i) = 0 Multiply (5 + 6i) * (-4 + 7i) (5(-4 + 7i) + 6i * (-4 + 7i)) = 0 ((-4 * 5 + 7i * 5) + 6i * (-4 + 7i)) = 0 ((-20 + 35i) + 6i * (-4 + 7i)) = 0 (-20 + 35i + (-4 * 6i + 7i * 6i)) = 0 (-20 + 35i + (-24i + 42i2)) = 0 Combine like terms: 35i + -24i = 11i (-20 + 11i + 42i2) = 0 Solving -20 + 11i + 42i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + -6i)(4 + -7i) = 0Subproblem 1
Set the factor '(-5 + -6i)' equal to zero and attempt to solve: Simplifying -5 + -6i = 0 Solving -5 + -6i = 0 Move all terms containing i to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -6i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6i = 0 + 5 -6i = 0 + 5 Combine like terms: 0 + 5 = 5 -6i = 5 Divide each side by '-6'. i = -0.8333333333 Simplifying i = -0.8333333333Subproblem 2
Set the factor '(4 + -7i)' equal to zero and attempt to solve: Simplifying 4 + -7i = 0 Solving 4 + -7i = 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 + -7i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7i = 0 + -4 -7i = 0 + -4 Combine like terms: 0 + -4 = -4 -7i = -4 Divide each side by '-7'. i = 0.5714285714 Simplifying i = 0.5714285714Solution
i = {-0.8333333333, 0.5714285714}
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