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Simplifying 0 = (3 + -2i)(3 + -2i) Multiply (3 + -2i) * (3 + -2i) 0 = (3(3 + -2i) + -2i * (3 + -2i)) 0 = ((3 * 3 + -2i * 3) + -2i * (3 + -2i)) 0 = ((9 + -6i) + -2i * (3 + -2i)) 0 = (9 + -6i + (3 * -2i + -2i * -2i)) 0 = (9 + -6i + (-6i + 4i2)) Combine like terms: -6i + -6i = -12i 0 = (9 + -12i + 4i2) Solving 0 = 9 + -12i + 4i2 Solving for variable 'i'. Combine like terms: 0 + -9 = -9 -9 + 12i + -4i2 = 9 + -12i + 4i2 + -9 + 12i + -4i2 Reorder the terms: -9 + 12i + -4i2 = 9 + -9 + -12i + 12i + 4i2 + -4i2 Combine like terms: 9 + -9 = 0 -9 + 12i + -4i2 = 0 + -12i + 12i + 4i2 + -4i2 -9 + 12i + -4i2 = -12i + 12i + 4i2 + -4i2 Combine like terms: -12i + 12i = 0 -9 + 12i + -4i2 = 0 + 4i2 + -4i2 -9 + 12i + -4i2 = 4i2 + -4i2 Combine like terms: 4i2 + -4i2 = 0 -9 + 12i + -4i2 = 0 Factor a trinomial. (-3 + 2i)(3 + -2i) = 0Subproblem 1
Set the factor '(-3 + 2i)' equal to zero and attempt to solve: Simplifying -3 + 2i = 0 Solving -3 + 2i = 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 + 2i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2i = 0 + 3 2i = 0 + 3 Combine like terms: 0 + 3 = 3 2i = 3 Divide each side by '2'. i = 1.5 Simplifying i = 1.5Subproblem 2
Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 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 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Solution
i = {1.5, 1.5}
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