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Simplifying (-4 + 5i)(-3 + 5i) = 0 Multiply (-4 + 5i) * (-3 + 5i) (-4(-3 + 5i) + 5i * (-3 + 5i)) = 0 ((-3 * -4 + 5i * -4) + 5i * (-3 + 5i)) = 0 ((12 + -20i) + 5i * (-3 + 5i)) = 0 (12 + -20i + (-3 * 5i + 5i * 5i)) = 0 (12 + -20i + (-15i + 25i2)) = 0 Combine like terms: -20i + -15i = -35i (12 + -35i + 25i2) = 0 Solving 12 + -35i + 25i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -5i)(4 + -5i) = 0Subproblem 1
Set the factor '(3 + -5i)' equal to zero and attempt to solve: Simplifying 3 + -5i = 0 Solving 3 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5i = 0 + -3 -5i = 0 + -3 Combine like terms: 0 + -3 = -3 -5i = -3 Divide each side by '-5'. i = 0.6 Simplifying i = 0.6Subproblem 2
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 = 0.8Solution
i = {0.6, 0.8}
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