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Simplifying (2 + 5i)(1 + -1i) = 0 Multiply (2 + 5i) * (1 + -1i) (2(1 + -1i) + 5i * (1 + -1i)) = 0 ((1 * 2 + -1i * 2) + 5i * (1 + -1i)) = 0 ((2 + -2i) + 5i * (1 + -1i)) = 0 (2 + -2i + (1 * 5i + -1i * 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. (1 + -1i)(2 + 5i) = 0Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 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 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Subproblem 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 = {1, -0.4}
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