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Simplifying (7 + -2i)(3 + 4i) = 0 Multiply (7 + -2i) * (3 + 4i) (7(3 + 4i) + -2i * (3 + 4i)) = 0 ((3 * 7 + 4i * 7) + -2i * (3 + 4i)) = 0 ((21 + 28i) + -2i * (3 + 4i)) = 0 (21 + 28i + (3 * -2i + 4i * -2i)) = 0 (21 + 28i + (-6i + -8i2)) = 0 Combine like terms: 28i + -6i = 22i (21 + 22i + -8i2) = 0 Solving 21 + 22i + -8i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -2i)(3 + 4i) = 0Subproblem 1
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 = 3.5Subproblem 2
Set the factor '(3 + 4i)' equal to zero and attempt to solve: Simplifying 3 + 4i = 0 Solving 3 + 4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4i = 0 + -3 4i = 0 + -3 Combine like terms: 0 + -3 = -3 4i = -3 Divide each side by '4'. i = -0.75 Simplifying i = -0.75Solution
i = {3.5, -0.75}
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