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Simplifying (4 + -5i)(-2 + 7i) = 0 Multiply (4 + -5i) * (-2 + 7i) (4(-2 + 7i) + -5i * (-2 + 7i)) = 0 ((-2 * 4 + 7i * 4) + -5i * (-2 + 7i)) = 0 ((-8 + 28i) + -5i * (-2 + 7i)) = 0 (-8 + 28i + (-2 * -5i + 7i * -5i)) = 0 (-8 + 28i + (10i + -35i2)) = 0 Combine like terms: 28i + 10i = 38i (-8 + 38i + -35i2) = 0 Solving -8 + 38i + -35i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + 5i)(2 + -7i) = 0Subproblem 1
Set the factor '(-4 + 5i)' equal to zero and attempt to solve: Simplifying -4 + 5i = 0 Solving -4 + 5i = 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 + 5i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5i = 0 + 4 5i = 0 + 4 Combine like terms: 0 + 4 = 4 5i = 4 Divide each side by '5'. i = 0.8 Simplifying i = 0.8Subproblem 2
Set the factor '(2 + -7i)' equal to zero and attempt to solve: Simplifying 2 + -7i = 0 Solving 2 + -7i = 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 + -7i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7i = 0 + -2 -7i = 0 + -2 Combine like terms: 0 + -2 = -2 -7i = -2 Divide each side by '-7'. i = 0.2857142857 Simplifying i = 0.2857142857Solution
i = {0.8, 0.2857142857}
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