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Simplifying (7 + 2i)(4 + -7i) = 0 Multiply (7 + 2i) * (4 + -7i) (7(4 + -7i) + 2i * (4 + -7i)) = 0 ((4 * 7 + -7i * 7) + 2i * (4 + -7i)) = 0 ((28 + -49i) + 2i * (4 + -7i)) = 0 (28 + -49i + (4 * 2i + -7i * 2i)) = 0 (28 + -49i + (8i + -14i2)) = 0 Combine like terms: -49i + 8i = -41i (28 + -41i + -14i2) = 0 Solving 28 + -41i + -14i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -7i)(7 + 2i) = 0Subproblem 1
Set the factor '(4 + -7i)' equal to zero and attempt to solve: Simplifying 4 + -7i = 0 Solving 4 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7i = 0 + -4 -7i = 0 + -4 Combine like terms: 0 + -4 = -4 -7i = -4 Divide each side by '-7'. i = 0.5714285714 Simplifying i = 0.5714285714Subproblem 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 = {0.5714285714, -3.5}
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