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Simplifying (-2 + 3i)(5 + -7i) = 0 Multiply (-2 + 3i) * (5 + -7i) (-2(5 + -7i) + 3i * (5 + -7i)) = 0 ((5 * -2 + -7i * -2) + 3i * (5 + -7i)) = 0 ((-10 + 14i) + 3i * (5 + -7i)) = 0 (-10 + 14i + (5 * 3i + -7i * 3i)) = 0 (-10 + 14i + (15i + -21i2)) = 0 Combine like terms: 14i + 15i = 29i (-10 + 29i + -21i2) = 0 Solving -10 + 29i + -21i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + 7i)(2 + -3i) = 0Subproblem 1
Set the factor '(-5 + 7i)' equal to zero and attempt to solve: Simplifying -5 + 7i = 0 Solving -5 + 7i = 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 + 7i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 7i = 0 + 5 7i = 0 + 5 Combine like terms: 0 + 5 = 5 7i = 5 Divide each side by '7'. i = 0.7142857143 Simplifying i = 0.7142857143Subproblem 2
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 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 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Solution
i = {0.7142857143, 0.6666666667}
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