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Simplifying (5 + -13i)(5 + -13i) = 0 Multiply (5 + -13i) * (5 + -13i) (5(5 + -13i) + -13i * (5 + -13i)) = 0 ((5 * 5 + -13i * 5) + -13i * (5 + -13i)) = 0 ((25 + -65i) + -13i * (5 + -13i)) = 0 (25 + -65i + (5 * -13i + -13i * -13i)) = 0 (25 + -65i + (-65i + 169i2)) = 0 Combine like terms: -65i + -65i = -130i (25 + -130i + 169i2) = 0 Solving 25 + -130i + 169i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -13i)(5 + -13i) = 0Subproblem 1
Set the factor '(5 + -13i)' equal to zero and attempt to solve: Simplifying 5 + -13i = 0 Solving 5 + -13i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -13i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -13i = 0 + -5 -13i = 0 + -5 Combine like terms: 0 + -5 = -5 -13i = -5 Divide each side by '-13'. i = 0.3846153846 Simplifying i = 0.3846153846Subproblem 2
Set the factor '(5 + -13i)' equal to zero and attempt to solve: Simplifying 5 + -13i = 0 Solving 5 + -13i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -13i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -13i = 0 + -5 -13i = 0 + -5 Combine like terms: 0 + -5 = -5 -13i = -5 Divide each side by '-13'. i = 0.3846153846 Simplifying i = 0.3846153846Solution
i = {0.3846153846, 0.3846153846}
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