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Simplifying (-4 + 4i)(-3 + 3i) = 0 Multiply (-4 + 4i) * (-3 + 3i) (-4(-3 + 3i) + 4i * (-3 + 3i)) = 0 ((-3 * -4 + 3i * -4) + 4i * (-3 + 3i)) = 0 ((12 + -12i) + 4i * (-3 + 3i)) = 0 (12 + -12i + (-3 * 4i + 3i * 4i)) = 0 (12 + -12i + (-12i + 12i2)) = 0 Combine like terms: -12i + -12i = -24i (12 + -24i + 12i2) = 0 Solving 12 + -24i + 12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '12'. 12(1 + -2i + i2) = 0 Factor a trinomial. 12((1 + -1i)(1 + -1i)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Subproblem 2
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Solution
i = {1, 1}
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