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Simplifying (-3 + 2i)(-3 + -7i) = 0 Multiply (-3 + 2i) * (-3 + -7i) (-3(-3 + -7i) + 2i * (-3 + -7i)) = 0 ((-3 * -3 + -7i * -3) + 2i * (-3 + -7i)) = 0 ((9 + 21i) + 2i * (-3 + -7i)) = 0 (9 + 21i + (-3 * 2i + -7i * 2i)) = 0 (9 + 21i + (-6i + -14i2)) = 0 Combine like terms: 21i + -6i = 15i (9 + 15i + -14i2) = 0 Solving 9 + 15i + -14i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -2i)(3 + 7i) = 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 + 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 = -0.4285714286Solution
i = {1.5, -0.4285714286}
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