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Simplifying (2 + i) + -1(4 + -6i)(-3 + 3i) = 0 Remove parenthesis around (2 + i) 2 + i + -1(4 + -6i)(-3 + 3i) = 0 Multiply (4 + -6i) * (-3 + 3i) 2 + i + -1(4(-3 + 3i) + -6i * (-3 + 3i)) = 0 2 + i + -1((-3 * 4 + 3i * 4) + -6i * (-3 + 3i)) = 0 2 + i + -1((-12 + 12i) + -6i * (-3 + 3i)) = 0 2 + i + -1(-12 + 12i + (-3 * -6i + 3i * -6i)) = 0 2 + i + -1(-12 + 12i + (18i + -18i2)) = 0 Combine like terms: 12i + 18i = 30i 2 + i + -1(-12 + 30i + -18i2) = 0 2 + i + (-12 * -1 + 30i * -1 + -18i2 * -1) = 0 2 + i + (12 + -30i + 18i2) = 0 Reorder the terms: 2 + 12 + i + -30i + 18i2 = 0 Combine like terms: 2 + 12 = 14 14 + i + -30i + 18i2 = 0 Combine like terms: i + -30i = -29i 14 + -29i + 18i2 = 0 Solving 14 + -29i + 18i2 = 0 Solving for variable 'i'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.7777777778 + -1.611111111i + i2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + -1.611111111i + -0.7777777778 + i2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + -1.611111111i + i2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + -1.611111111i + i2 = 0 + -0.7777777778 -1.611111111i + i2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 -1.611111111i + i2 = -0.7777777778 The i term is -1.611111111i. Take half its coefficient (-0.8055555555). Square it (0.6489197530) and add it to both sides. Add '0.6489197530' to each side of the equation. -1.611111111i + 0.6489197530 + i2 = -0.7777777778 + 0.6489197530 Reorder the terms: 0.6489197530 + -1.611111111i + i2 = -0.7777777778 + 0.6489197530 Combine like terms: -0.7777777778 + 0.6489197530 = -0.1288580248 0.6489197530 + -1.611111111i + i2 = -0.1288580248 Factor a perfect square on the left side: (i + -0.8055555555)(i + -0.8055555555) = -0.1288580248 Can't calculate square root of the right side. The solution to this equation could not be determined.
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