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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 out the Greatest Common Factor (GCF), '-1'. -1(2 + 15i + 25i2) = 0 Factor a trinomial. -1((2 + 5i)(1 + 5i)) = 0 Ignore the factor -1.Subproblem 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 '(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 = {-0.4, -0.2}
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