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Simplifying (2i + -1)(3i + 1) = -7 + -1i Reorder the terms: (-1 + 2i)(3i + 1) = -7 + -1i Reorder the terms: (-1 + 2i)(1 + 3i) = -7 + -1i Multiply (-1 + 2i) * (1 + 3i) (-1(1 + 3i) + 2i * (1 + 3i)) = -7 + -1i ((1 * -1 + 3i * -1) + 2i * (1 + 3i)) = -7 + -1i ((-1 + -3i) + 2i * (1 + 3i)) = -7 + -1i (-1 + -3i + (1 * 2i + 3i * 2i)) = -7 + -1i (-1 + -3i + (2i + 6i2)) = -7 + -1i Combine like terms: -3i + 2i = -1i (-1 + -1i + 6i2) = -7 + -1i Add 'i' to each side of the equation. -1 + -1i + i + 6i2 = -7 + -1i + i Combine like terms: -1i + i = 0 -1 + 0 + 6i2 = -7 + -1i + i -1 + 6i2 = -7 + -1i + i Combine like terms: -1i + i = 0 -1 + 6i2 = -7 + 0 -1 + 6i2 = -7 Solving -1 + 6i2 = -7 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 6i2 = -7 + 1 Combine like terms: -1 + 1 = 0 0 + 6i2 = -7 + 1 6i2 = -7 + 1 Combine like terms: -7 + 1 = -6 6i2 = -6 Divide each side by '6'. i2 = -1 Simplifying i2 = -1 Reorder the terms: 1 + i2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + i2 = 0 The solution to this equation could not be determined.
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