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Simplifying (-4 + 5i)(-7 + 4i) = 0 Multiply (-4 + 5i) * (-7 + 4i) (-4(-7 + 4i) + 5i * (-7 + 4i)) = 0 ((-7 * -4 + 4i * -4) + 5i * (-7 + 4i)) = 0 ((28 + -16i) + 5i * (-7 + 4i)) = 0 (28 + -16i + (-7 * 5i + 4i * 5i)) = 0 (28 + -16i + (-35i + 20i2)) = 0 Combine like terms: -16i + -35i = -51i (28 + -51i + 20i2) = 0 Solving 28 + -51i + 20i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -5i)(7 + -4i) = 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 '(7 + -4i)' equal to zero and attempt to solve: Simplifying 7 + -4i = 0 Solving 7 + -4i = 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 + -4i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4i = 0 + -7 -4i = 0 + -7 Combine like terms: 0 + -7 = -7 -4i = -7 Divide each side by '-4'. i = 1.75 Simplifying i = 1.75Solution
i = {0.8, 1.75}
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