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Simplifying (2 + -5i)(p + q) * i = 29i Reorder the terms for easier multiplication: i(2 + -5i)(p + q) = 29i Multiply (2 + -5i) * (p + q) i(2(p + q) + -5i * (p + q)) = 29i i((p * 2 + q * 2) + -5i * (p + q)) = 29i i((2p + 2q) + -5i * (p + q)) = 29i i(2p + 2q + (p * -5i + q * -5i)) = 29i i(2p + 2q + (-5ip + -5iq)) = 29i Reorder the terms: i(-5ip + -5iq + 2p + 2q) = 29i i(-5ip + -5iq + 2p + 2q) = 29i (-5ip * i + -5iq * i + 2p * i + 2q * i) = 29i Reorder the terms: (2ip + 2iq + -5i2p + -5i2q) = 29i (2ip + 2iq + -5i2p + -5i2q) = 29i Solving 2ip + 2iq + -5i2p + -5i2q = 29i Solving for variable 'i'. Reorder the terms: -29i + 2ip + 2iq + -5i2p + -5i2q = 29i + -29i Combine like terms: 29i + -29i = 0 -29i + 2ip + 2iq + -5i2p + -5i2q = 0 Factor out the Greatest Common Factor (GCF), 'i'. i(-29 + 2p + 2q + -5ip + -5iq) = 0Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 2
Set the factor '(-29 + 2p + 2q + -5ip + -5iq)' equal to zero and attempt to solve: Simplifying -29 + 2p + 2q + -5ip + -5iq = 0 Reorder the terms: -29 + -5ip + -5iq + 2p + 2q = 0 Solving -29 + -5ip + -5iq + 2p + 2q = 0 Move all terms containing i to the left, all other terms to the right. Add '29' to each side of the equation. -29 + -5ip + -5iq + 2p + 29 + 2q = 0 + 29 Reorder the terms: -29 + 29 + -5ip + -5iq + 2p + 2q = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -5ip + -5iq + 2p + 2q = 0 + 29 -5ip + -5iq + 2p + 2q = 0 + 29 Combine like terms: 0 + 29 = 29 -5ip + -5iq + 2p + 2q = 29 Add '-2p' to each side of the equation. -5ip + -5iq + 2p + -2p + 2q = 29 + -2p Combine like terms: 2p + -2p = 0 -5ip + -5iq + 0 + 2q = 29 + -2p -5ip + -5iq + 2q = 29 + -2p Add '-2q' to each side of the equation. -5ip + -5iq + 2q + -2q = 29 + -2p + -2q Combine like terms: 2q + -2q = 0 -5ip + -5iq + 0 = 29 + -2p + -2q -5ip + -5iq = 29 + -2p + -2q The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
i = {0}
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