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Simplifying (2 + -5i)(1 + -5i) = 0 Multiply (2 + -5i) * (1 + -5i) (2(1 + -5i) + -5i * (1 + -5i)) = 0 ((1 * 2 + -5i * 2) + -5i * (1 + -5i)) = 0 ((2 + -10i) + -5i * (1 + -5i)) = 0 (2 + -10i + (1 * -5i + -5i * -5i)) = 0 (2 + -10i + (-5i + 25i2)) = 0 Combine like terms: -10i + -5i = -15i (2 + -15i + 25i2) = 0 Solving 2 + -15i + 25i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + -5i)(2 + -5i) = 0Subproblem 1
Set the factor '(1 + -5i)' equal to zero and attempt to solve: Simplifying 1 + -5i = 0 Solving 1 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5i = 0 + -1 -5i = 0 + -1 Combine like terms: 0 + -1 = -1 -5i = -1 Divide each side by '-5'. i = 0.2 Simplifying i = 0.2Subproblem 2
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 = 0.4Solution
i = {0.2, 0.4}
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