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Simplifying (7 + -5i)(2 + 3i) = 0 Multiply (7 + -5i) * (2 + 3i) (7(2 + 3i) + -5i * (2 + 3i)) = 0 ((2 * 7 + 3i * 7) + -5i * (2 + 3i)) = 0 ((14 + 21i) + -5i * (2 + 3i)) = 0 (14 + 21i + (2 * -5i + 3i * -5i)) = 0 (14 + 21i + (-10i + -15i2)) = 0 Combine like terms: 21i + -10i = 11i (14 + 11i + -15i2) = 0 Solving 14 + 11i + -15i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -5i)(2 + 3i) = 0Subproblem 1
Set the factor '(7 + -5i)' equal to zero and attempt to solve: Simplifying 7 + -5i = 0 Solving 7 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5i = 0 + -7 -5i = 0 + -7 Combine like terms: 0 + -7 = -7 -5i = -7 Divide each side by '-5'. i = 1.4 Simplifying i = 1.4Subproblem 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 = {1.4, -0.6666666667}
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