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Simplifying (-3i)(3i) + -1(2 + 2i) = 0 Remove parenthesis around (-3i) -3i(3i) + -1(2 + 2i) = 0 Remove parenthesis around (3i) -3i * 3i + -1(2 + 2i) = 0 Reorder the terms for easier multiplication: -3 * 3i * i + -1(2 + 2i) = 0 Multiply -3 * 3 -9i * i + -1(2 + 2i) = 0 Multiply i * i -9i2 + -1(2 + 2i) = 0 -9i2 + (2 * -1 + 2i * -1) = 0 -9i2 + (-2 + -2i) = 0 Reorder the terms: -2 + -2i + -9i2 = 0 Solving -2 + -2i + -9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 2i + 9i2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 2i + 9i2)' equal to zero and attempt to solve: Simplifying 2 + 2i + 9i2 = 0 Solving 2 + 2i + 9i2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + 0.2222222222i + i2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 0.2222222222i + -0.2222222222 + i2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 0.2222222222i + i2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 0.2222222222i + i2 = 0 + -0.2222222222 0.2222222222i + i2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 0.2222222222i + i2 = -0.2222222222 The i term is 0.2222222222i. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222i + 0.01234567901 + i2 = -0.2222222222 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222i + i2 = -0.2222222222 + 0.01234567901 Combine like terms: -0.2222222222 + 0.01234567901 = -0.20987654319 0.01234567901 + 0.2222222222i + i2 = -0.20987654319 Factor a perfect square on the left side: (i + 0.1111111111)(i + 0.1111111111) = -0.20987654319 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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