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Simplifying (8 + 5i)(2 + -5i) = 0 Multiply (8 + 5i) * (2 + -5i) (8(2 + -5i) + 5i * (2 + -5i)) = 0 ((2 * 8 + -5i * 8) + 5i * (2 + -5i)) = 0 ((16 + -40i) + 5i * (2 + -5i)) = 0 (16 + -40i + (2 * 5i + -5i * 5i)) = 0 (16 + -40i + (10i + -25i2)) = 0 Combine like terms: -40i + 10i = -30i (16 + -30i + -25i2) = 0 Solving 16 + -30i + -25i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -5i)(8 + 5i) = 0Subproblem 1
Set the factor '(2 + -5i)' equal to zero and attempt to solve: Simplifying 2 + -5i = 0 Solving 2 + -5i = 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 + -5i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5i = 0 + -2 -5i = 0 + -2 Combine like terms: 0 + -2 = -2 -5i = -2 Divide each side by '-5'. i = 0.4 Simplifying i = 0.4Subproblem 2
Set the factor '(8 + 5i)' equal to zero and attempt to solve: Simplifying 8 + 5i = 0 Solving 8 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 5i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5i = 0 + -8 5i = 0 + -8 Combine like terms: 0 + -8 = -8 5i = -8 Divide each side by '5'. i = -1.6 Simplifying i = -1.6Solution
i = {0.4, -1.6}
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