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Simplifying (7 + 2i)(5 + -2i) = 0 Multiply (7 + 2i) * (5 + -2i) (7(5 + -2i) + 2i * (5 + -2i)) = 0 ((5 * 7 + -2i * 7) + 2i * (5 + -2i)) = 0 ((35 + -14i) + 2i * (5 + -2i)) = 0 (35 + -14i + (5 * 2i + -2i * 2i)) = 0 (35 + -14i + (10i + -4i2)) = 0 Combine like terms: -14i + 10i = -4i (35 + -4i + -4i2) = 0 Solving 35 + -4i + -4i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -2i)(7 + 2i) = 0Subproblem 1
Set the factor '(5 + -2i)' equal to zero and attempt to solve: Simplifying 5 + -2i = 0 Solving 5 + -2i = 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 + -2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2i = 0 + -5 -2i = 0 + -5 Combine like terms: 0 + -5 = -5 -2i = -5 Divide each side by '-2'. i = 2.5 Simplifying i = 2.5Subproblem 2
Set the factor '(7 + 2i)' equal to zero and attempt to solve: Simplifying 7 + 2i = 0 Solving 7 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2i = 0 + -7 2i = 0 + -7 Combine like terms: 0 + -7 = -7 2i = -7 Divide each side by '2'. i = -3.5 Simplifying i = -3.5Solution
i = {2.5, -3.5}
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