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