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Simplifying -1(3 + i)(7 + -3i) = 0 Multiply (3 + i) * (7 + -3i) -1(3(7 + -3i) + i(7 + -3i)) = 0 -1((7 * 3 + -3i * 3) + i(7 + -3i)) = 0 -1((21 + -9i) + i(7 + -3i)) = 0 -1(21 + -9i + (7 * i + -3i * i)) = 0 -1(21 + -9i + (7i + -3i2)) = 0 Combine like terms: -9i + 7i = -2i -1(21 + -2i + -3i2) = 0 (21 * -1 + -2i * -1 + -3i2 * -1) = 0 (-21 + 2i + 3i2) = 0 Solving -21 + 2i + 3i2 = 0 Solving for variable 'i'. Factor a trinomial. (-3 + -1i)(7 + -3i) = 0Subproblem 1
Set the factor '(-3 + -1i)' equal to zero and attempt to solve: Simplifying -3 + -1i = 0 Solving -3 + -1i = 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 + -1i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1i = 0 + 3 -1i = 0 + 3 Combine like terms: 0 + 3 = 3 -1i = 3 Divide each side by '-1'. i = -3 Simplifying i = -3Subproblem 2
Set the factor '(7 + -3i)' equal to zero and attempt to solve: Simplifying 7 + -3i = 0 Solving 7 + -3i = 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 + -3i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3i = 0 + -7 -3i = 0 + -7 Combine like terms: 0 + -7 = -7 -3i = -7 Divide each side by '-3'. i = 2.333333333 Simplifying i = 2.333333333Solution
i = {-3, 2.333333333}
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