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i) Solve the quadratic Equation -x^(2)+x-2=0 (IMP-2014) ii) Express ' r ' in the form r(cos theta+i sin theta)

22.\newlinei) Solve the quadratic Equation −x2+x−2=0 -x^{2}+x-2=0 (IMP−2014-2014)\newlineii) Express ' r r ' in the form r(cos⁡θ+isin⁡θ) r(\cos \theta+i \sin \theta)

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Q. 22.\newlinei) Solve the quadratic Equation −x2+x−2=0 -x^{2}+x-2=0 (IMP−2014-2014)\newlineii) Express ' r r ' in the form r(cos⁡θ+isin⁡θ) r(\cos \theta+i \sin \theta)
  1. Identify equation type: Identify the type of equation and apply the quadratic formula where a=−1a = -1, b=1b = 1, and c=−2c = -2.
  2. Apply quadratic formula: Simplify the square root and solve for xx.
  3. Simplify square root: Express the roots in the form r(cos⁡θ+isin⁡θ)r(\cos \theta + i \sin \theta).
  4. Express roots: Calculate θ\theta for the expression r(cos⁡θ+isin⁡θ)r(\cos \theta + i \sin \theta).
  5. Calculate theta: Write the final expression for rr in the form r(cos⁡θ+isin⁡θ)r(\cos \theta + i \sin \theta).

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