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Simplifying (2 + -5i)(1 + i) = 0 Multiply (2 + -5i) * (1 + i) (2(1 + i) + -5i * (1 + i)) = 0 ((1 * 2 + i * 2) + -5i * (1 + i)) = 0 ((2 + 2i) + -5i * (1 + i)) = 0 (2 + 2i + (1 * -5i + i * -5i)) = 0 (2 + 2i + (-5i + -5i2)) = 0 Combine like terms: 2i + -5i = -3i (2 + -3i + -5i2) = 0 Solving 2 + -3i + -5i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -5i)(1 + i) = 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 '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 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 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {0.4, -1}
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