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Simplifying (-3 + 7i)(-7 + 8i) = 0 Multiply (-3 + 7i) * (-7 + 8i) (-3(-7 + 8i) + 7i * (-7 + 8i)) = 0 ((-7 * -3 + 8i * -3) + 7i * (-7 + 8i)) = 0 ((21 + -24i) + 7i * (-7 + 8i)) = 0 (21 + -24i + (-7 * 7i + 8i * 7i)) = 0 (21 + -24i + (-49i + 56i2)) = 0 Combine like terms: -24i + -49i = -73i (21 + -73i + 56i2) = 0 Solving 21 + -73i + 56i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -7i)(7 + -8i) = 0Subproblem 1
Set the factor '(3 + -7i)' equal to zero and attempt to solve: Simplifying 3 + -7i = 0 Solving 3 + -7i = 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 + -7i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7i = 0 + -3 -7i = 0 + -3 Combine like terms: 0 + -3 = -3 -7i = -3 Divide each side by '-7'. i = 0.4285714286 Simplifying i = 0.4285714286Subproblem 2
Set the factor '(7 + -8i)' equal to zero and attempt to solve: Simplifying 7 + -8i = 0 Solving 7 + -8i = 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 + -8i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8i = 0 + -7 -8i = 0 + -7 Combine like terms: 0 + -7 = -7 -8i = -7 Divide each side by '-8'. i = 0.875 Simplifying i = 0.875Solution
i = {0.4285714286, 0.875}
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