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Simplifying (-2 + 7i)(-9 + 2i) = 0 Multiply (-2 + 7i) * (-9 + 2i) (-2(-9 + 2i) + 7i * (-9 + 2i)) = 0 ((-9 * -2 + 2i * -2) + 7i * (-9 + 2i)) = 0 ((18 + -4i) + 7i * (-9 + 2i)) = 0 (18 + -4i + (-9 * 7i + 2i * 7i)) = 0 (18 + -4i + (-63i + 14i2)) = 0 Combine like terms: -4i + -63i = -67i (18 + -67i + 14i2) = 0 Solving 18 + -67i + 14i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -7i)(9 + -2i) = 0Subproblem 1
Set the factor '(2 + -7i)' equal to zero and attempt to solve: Simplifying 2 + -7i = 0 Solving 2 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7i = 0 + -2 -7i = 0 + -2 Combine like terms: 0 + -2 = -2 -7i = -2 Divide each side by '-7'. i = 0.2857142857 Simplifying i = 0.2857142857Subproblem 2
Set the factor '(9 + -2i)' equal to zero and attempt to solve: Simplifying 9 + -2i = 0 Solving 9 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2i = 0 + -9 -2i = 0 + -9 Combine like terms: 0 + -9 = -9 -2i = -9 Divide each side by '-2'. i = 4.5 Simplifying i = 4.5Solution
i = {0.2857142857, 4.5}
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