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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 = 0 (12 + 0 + -12i2) = 0 (12 + -12i2) = 0 Solving 12 + -12i2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -12i2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -12i2 = 0 + -12 -12i2 = 0 + -12 Combine like terms: 0 + -12 = -12 -12i2 = -12 Divide each side by '-12'. i2 = 1 Simplifying i2 = 1 Take the square root of each side: i = {-1, 1}
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