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Simplifying (-1 + 5i)(-1 + 5i) = 0 Multiply (-1 + 5i) * (-1 + 5i) (-1(-1 + 5i) + 5i * (-1 + 5i)) = 0 ((-1 * -1 + 5i * -1) + 5i * (-1 + 5i)) = 0 ((1 + -5i) + 5i * (-1 + 5i)) = 0 (1 + -5i + (-1 * 5i + 5i * 5i)) = 0 (1 + -5i + (-5i + 25i2)) = 0 Combine like terms: -5i + -5i = -10i (1 + -10i + 25i2) = 0 Solving 1 + -10i + 25i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + -5i)(1 + -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 '(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 = 0.2Solution
i = {0.2, 0.2}
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