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Simplifying (7 + -4i)(5 + -2i) = 0 Multiply (7 + -4i) * (5 + -2i) (7(5 + -2i) + -4i * (5 + -2i)) = 0 ((5 * 7 + -2i * 7) + -4i * (5 + -2i)) = 0 ((35 + -14i) + -4i * (5 + -2i)) = 0 (35 + -14i + (5 * -4i + -2i * -4i)) = 0 (35 + -14i + (-20i + 8i2)) = 0 Combine like terms: -14i + -20i = -34i (35 + -34i + 8i2) = 0 Solving 35 + -34i + 8i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -4i)(5 + -2i) = 0Subproblem 1
Set the factor '(7 + -4i)' equal to zero and attempt to solve: Simplifying 7 + -4i = 0 Solving 7 + -4i = 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 + -4i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4i = 0 + -7 -4i = 0 + -7 Combine like terms: 0 + -7 = -7 -4i = -7 Divide each side by '-4'. i = 1.75 Simplifying i = 1.75Subproblem 2
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 = 2.5Solution
i = {1.75, 2.5}
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