Roots of x²+2x+2=0 — Find α¹⁵+β¹⁵
If α, β are the roots of x²+2x+2=0, find α¹⁵+β¹⁵ by converting the complex roots to polar form and using De Moivre’s theorem.
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|z|≤1: Minimum Value of |z+1/2(3+4i)|
If z is a complex number with |z|≤1, find the minimum value of |z+1/2(3+4i)| by interpreting it as the distance from a fixed point to the unit disk.
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α,β Roots of x²−x+1=0 — Find α¹⁰¹+β¹⁰⁷
If α,β are the distinct complex roots of x²−x+1=0, find α¹⁰¹+β¹⁰⁷ by recognising the roots as negatives of cube roots of unity.
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A∩B for |(z+1)/(z−1)|<1 and arg((z−1)/(z+1))=2π/3
Let A: |(z+1)/(z−1)|<1 and B: arg((z−1)/(z+1))=2π/3 in the complex plane. Find A∩B by converting both conditions into geometric loci.
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Complex Roots of x²-(3-2i)x-(2i-2)=0, Find αγ+βδ
A quadratic with complex coefficients and complex roots is easier factorised directly than approached through Vieta’s formulas. JEE Main 2025, solved.