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Simplifying (i + 3) + i(2i + -4) = 0 Reorder the terms: (3 + i) + i(2i + -4) = 0 Remove parenthesis around (3 + i) 3 + i + i(2i + -4) = 0 Reorder the terms: 3 + i + i(-4 + 2i) = 0 3 + i + (-4 * i + 2i * i) = 0 3 + i + (-4i + 2i2) = 0 Combine like terms: i + -4i = -3i 3 + -3i + 2i2 = 0 Solving 3 + -3i + 2i2 = 0 Solving for variable 'i'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -1.5i + i2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -1.5i + -1.5 + i2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -1.5i + i2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -1.5i + i2 = 0 + -1.5 -1.5i + i2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -1.5i + i2 = -1.5 The i term is -1.5i. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5i + 0.5625 + i2 = -1.5 + 0.5625 Reorder the terms: 0.5625 + -1.5i + i2 = -1.5 + 0.5625 Combine like terms: -1.5 + 0.5625 = -0.9375 0.5625 + -1.5i + i2 = -0.9375 Factor a perfect square on the left side: (i + -0.75)(i + -0.75) = -0.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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