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Simplifying (1 + 2i)(4 + -1i) = 4 + -1i + 8i + -2i2 Multiply (1 + 2i) * (4 + -1i) (1(4 + -1i) + 2i * (4 + -1i)) = 4 + -1i + 8i + -2i2 ((4 * 1 + -1i * 1) + 2i * (4 + -1i)) = 4 + -1i + 8i + -2i2 ((4 + -1i) + 2i * (4 + -1i)) = 4 + -1i + 8i + -2i2 (4 + -1i + (4 * 2i + -1i * 2i)) = 4 + -1i + 8i + -2i2 (4 + -1i + (8i + -2i2)) = 4 + -1i + 8i + -2i2 Combine like terms: -1i + 8i = 7i (4 + 7i + -2i2) = 4 + -1i + 8i + -2i2 Combine like terms: -1i + 8i = 7i 4 + 7i + -2i2 = 4 + 7i + -2i2 Add '-4' to each side of the equation. 4 + 7i + -4 + -2i2 = 4 + 7i + -4 + -2i2 Reorder the terms: 4 + -4 + 7i + -2i2 = 4 + 7i + -4 + -2i2 Combine like terms: 4 + -4 = 0 0 + 7i + -2i2 = 4 + 7i + -4 + -2i2 7i + -2i2 = 4 + 7i + -4 + -2i2 Reorder the terms: 7i + -2i2 = 4 + -4 + 7i + -2i2 Combine like terms: 4 + -4 = 0 7i + -2i2 = 0 + 7i + -2i2 7i + -2i2 = 7i + -2i2 Add '-7i' to each side of the equation. 7i + -7i + -2i2 = 7i + -7i + -2i2 Combine like terms: 7i + -7i = 0 0 + -2i2 = 7i + -7i + -2i2 -2i2 = 7i + -7i + -2i2 Combine like terms: 7i + -7i = 0 -2i2 = 0 + -2i2 -2i2 = -2i2 Add '2i2' to each side of the equation. -2i2 + 2i2 = -2i2 + 2i2 Combine like terms: -2i2 + 2i2 = 0 0 = -2i2 + 2i2 Combine like terms: -2i2 + 2i2 = 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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