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Simplifying (1 + ai)(1 + -1ai) = 2 Multiply (1 + ai) * (1 + -1ai) (1(1 + -1ai) + ai(1 + -1ai)) = 2 ((1 * 1 + -1ai * 1) + ai(1 + -1ai)) = 2 ((1 + -1ai) + ai(1 + -1ai)) = 2 (1 + -1ai + (1 * ai + -1ai * ai)) = 2 (1 + -1ai + (1ai + -1a2i2)) = 2 Combine like terms: -1ai + 1ai = 0 (1 + 0 + -1a2i2) = 2 (1 + -1a2i2) = 2 Solving 1 + -1a2i2 = 2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1a2i2 = 2 + -1 Combine like terms: 1 + -1 = 0 0 + -1a2i2 = 2 + -1 -1a2i2 = 2 + -1 Combine like terms: 2 + -1 = 1 -1a2i2 = 1 Divide each side by '-1i2'. a2 = -1i-2 Simplifying a2 = -1i-2 Combine like terms: -1i-2 + i-2 = 0 a2 + i-2 = 0 Factor out the Greatest Common Factor (GCF), 'i-2'. i-2(a2i2 + 1) = 0Subproblem 1
Set the factor 'i-2' equal to zero and attempt to solve: Simplifying i-2 = 0 Solving i-2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1i-2' to each side of the equation. i-2 + -1i-2 = 0 + -1i-2 Remove the zero: 0 = -1i-2 Simplifying 0 = -1i-2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(a2i2 + 1)' equal to zero and attempt to solve: Simplifying a2i2 + 1 = 0 Reorder the terms: 1 + a2i2 = 0 Solving 1 + a2i2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a2i2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a2i2 = 0 + -1 a2i2 = 0 + -1 Combine like terms: 0 + -1 = -1 a2i2 = -1 Divide each side by 'i2'. a2 = -1i-2 Simplifying a2 = -1i-2 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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