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Simplifying (-4 + 7i)(7 + 4i) = 0 Multiply (-4 + 7i) * (7 + 4i) (-4(7 + 4i) + 7i * (7 + 4i)) = 0 ((7 * -4 + 4i * -4) + 7i * (7 + 4i)) = 0 ((-28 + -16i) + 7i * (7 + 4i)) = 0 (-28 + -16i + (7 * 7i + 4i * 7i)) = 0 (-28 + -16i + (49i + 28i2)) = 0 Combine like terms: -16i + 49i = 33i (-28 + 33i + 28i2) = 0 Solving -28 + 33i + 28i2 = 0 Solving for variable 'i'. Factor a trinomial. (-7 + -4i)(4 + -7i) = 0Subproblem 1
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 = -1.75Subproblem 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 = {-1.75, 0.5714285714}
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