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Simplifying 5z + -1 = (2 + -1i) * z + -2i Reorder the terms: -1 + 5z = (2 + -1i) * z + -2i Reorder the terms for easier multiplication: -1 + 5z = z(2 + -1i) + -2i -1 + 5z = (2 * z + -1i * z) + -2i Reorder the terms: -1 + 5z = (-1iz + 2z) + -2i -1 + 5z = (-1iz + 2z) + -2i Reorder the terms: -1 + 5z = -2i + -1iz + 2z Solving -1 + 5z = -2i + -1iz + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add 'iz' to each side of the equation. -1 + iz + 5z = -2i + -1iz + iz + 2z Combine like terms: -1iz + iz = 0 -1 + iz + 5z = -2i + 0 + 2z -1 + iz + 5z = -2i + 2z Add '-2z' to each side of the equation. -1 + iz + 5z + -2z = -2i + 2z + -2z Combine like terms: 5z + -2z = 3z -1 + iz + 3z = -2i + 2z + -2z Combine like terms: 2z + -2z = 0 -1 + iz + 3z = -2i + 0 -1 + iz + 3z = -2i Add '1' to each side of the equation. -1 + iz + 1 + 3z = 1 + -2i Reorder the terms: -1 + 1 + iz + 3z = 1 + -2i Combine like terms: -1 + 1 = 0 0 + iz + 3z = 1 + -2i iz + 3z = 1 + -2i Reorder the terms: -1 + 2i + iz + 3z = 1 + -2i + -1 + 2i Reorder the terms: -1 + 2i + iz + 3z = 1 + -1 + -2i + 2i Combine like terms: 1 + -1 = 0 -1 + 2i + iz + 3z = 0 + -2i + 2i -1 + 2i + iz + 3z = -2i + 2i Combine like terms: -2i + 2i = 0 -1 + 2i + iz + 3z = 0 The solution to this equation could not be determined.
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