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Simplifying (4 + 5i)(2 + 3i) = 0 Multiply (4 + 5i) * (2 + 3i) (4(2 + 3i) + 5i * (2 + 3i)) = 0 ((2 * 4 + 3i * 4) + 5i * (2 + 3i)) = 0 ((8 + 12i) + 5i * (2 + 3i)) = 0 (8 + 12i + (2 * 5i + 3i * 5i)) = 0 (8 + 12i + (10i + 15i2)) = 0 Combine like terms: 12i + 10i = 22i (8 + 22i + 15i2) = 0 Solving 8 + 22i + 15i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + 5i)(2 + 3i) = 0Subproblem 1
Set the factor '(4 + 5i)' equal to zero and attempt to solve: Simplifying 4 + 5i = 0 Solving 4 + 5i = 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 + 5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5i = 0 + -4 5i = 0 + -4 Combine like terms: 0 + -4 = -4 5i = -4 Divide each side by '5'. i = -0.8 Simplifying i = -0.8Subproblem 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 = {-0.8, -0.6666666667}
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