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Simplifying (9 + -2i)(-4 + -7i) = 0 Multiply (9 + -2i) * (-4 + -7i) (9(-4 + -7i) + -2i * (-4 + -7i)) = 0 ((-4 * 9 + -7i * 9) + -2i * (-4 + -7i)) = 0 ((-36 + -63i) + -2i * (-4 + -7i)) = 0 (-36 + -63i + (-4 * -2i + -7i * -2i)) = 0 (-36 + -63i + (8i + 14i2)) = 0 Combine like terms: -63i + 8i = -55i (-36 + -55i + 14i2) = 0 Solving -36 + -55i + 14i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + -7i)(9 + -2i) = 0Subproblem 1
Set the factor '(-4 + -7i)' equal to zero and attempt to solve: Simplifying -4 + -7i = 0 Solving -4 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -7i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7i = 0 + 4 -7i = 0 + 4 Combine like terms: 0 + 4 = 4 -7i = 4 Divide each side by '-7'. i = -0.5714285714 Simplifying i = -0.5714285714Subproblem 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 = {-0.5714285714, 4.5}
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