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Simplifying (3 + 7i)(-5 + 2i) = 0 Multiply (3 + 7i) * (-5 + 2i) (3(-5 + 2i) + 7i * (-5 + 2i)) = 0 ((-5 * 3 + 2i * 3) + 7i * (-5 + 2i)) = 0 ((-15 + 6i) + 7i * (-5 + 2i)) = 0 (-15 + 6i + (-5 * 7i + 2i * 7i)) = 0 (-15 + 6i + (-35i + 14i2)) = 0 Combine like terms: 6i + -35i = -29i (-15 + -29i + 14i2) = 0 Solving -15 + -29i + 14i2 = 0 Solving for variable 'i'. Factor a trinomial. (-3 + -7i)(5 + -2i) = 0Subproblem 1
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 = -0.4285714286Subproblem 2
Set the factor '(5 + -2i)' equal to zero and attempt to solve: Simplifying 5 + -2i = 0 Solving 5 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2i = 0 + -5 -2i = 0 + -5 Combine like terms: 0 + -5 = -5 -2i = -5 Divide each side by '-2'. i = 2.5 Simplifying i = 2.5Solution
i = {-0.4285714286, 2.5}
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