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Simplifying (7 + -4i)(2 + i) = 0 Multiply (7 + -4i) * (2 + i) (7(2 + i) + -4i * (2 + i)) = 0 ((2 * 7 + i * 7) + -4i * (2 + i)) = 0 ((14 + 7i) + -4i * (2 + i)) = 0 (14 + 7i + (2 * -4i + i * -4i)) = 0 (14 + 7i + (-8i + -4i2)) = 0 Combine like terms: 7i + -8i = -1i (14 + -1i + -4i2) = 0 Solving 14 + -1i + -4i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -4i)(2 + i) = 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 '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 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 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2Solution
i = {1.75, -2}
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