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Simplifying z2 + -1scrt(2) * z + (0.5 + -1i) = 0 Reorder the terms for easier multiplication: z2 + -1 * 2crst * z + (0.5 + -1i) = 0 Multiply -1 * 2 z2 + -2crst * z + (0.5 + -1i) = 0 Multiply crst * z z2 + -2crstz + (0.5 + -1i) = 0 Remove parenthesis around (0.5 + -1i) z2 + -2crstz + 0.5 + -1i = 0 Reorder the terms: 0.5 + -2crstz + -1i + z2 = 0 Solving 0.5 + -2crstz + -1i + z2 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -2crstz + -1i + -0.5 + z2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -2crstz + -1i + z2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -2crstz + -1i + z2 = 0 + -0.5 -2crstz + -1i + z2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -2crstz + -1i + z2 = -0.5 Add 'i' to each side of the equation. -2crstz + -1i + i + z2 = -0.5 + i Combine like terms: -1i + i = 0 -2crstz + 0 + z2 = -0.5 + i -2crstz + z2 = -0.5 + i Add '-1z2' to each side of the equation. -2crstz + z2 + -1z2 = -0.5 + i + -1z2 Combine like terms: z2 + -1z2 = 0 -2crstz + 0 = -0.5 + i + -1z2 -2crstz = -0.5 + i + -1z2 Divide each side by '-2rstz'. c = 0.25r-1s-1t-1z-1 + -0.5ir-1s-1t-1z-1 + 0.5r-1s-1t-1z Simplifying c = 0.25r-1s-1t-1z-1 + -0.5ir-1s-1t-1z-1 + 0.5r-1s-1t-1z Reorder the terms: c = -0.5ir-1s-1t-1z-1 + 0.25r-1s-1t-1z-1 + 0.5r-1s-1t-1z
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