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Simplifying (4 + -9i + -3in + 1) + 3ni = 5 + -9i Reorder the terms: (4 + 1 + -9i + -3in) + 3ni = 5 + -9i Combine like terms: 4 + 1 = 5 (5 + -9i + -3in) + 3ni = 5 + -9i Remove parenthesis around (5 + -9i + -3in) 5 + -9i + -3in + 3ni = 5 + -9i Combine like terms: -3in + 3in = 0 5 + -9i + 0 = 5 + -9i 5 + -9i = 5 + -9i Add '-5' to each side of the equation. 5 + -5 + -9i = 5 + -5 + -9i Combine like terms: 5 + -5 = 0 0 + -9i = 5 + -5 + -9i -9i = 5 + -5 + -9i Combine like terms: 5 + -5 = 0 -9i = 0 + -9i -9i = -9i Add '9i' to each side of the equation. -9i + 9i = -9i + 9i Combine like terms: -9i + 9i = 0 0 = -9i + 9i Combine like terms: -9i + 9i = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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