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((1+i)/(1-i))^4+((1-i)/(1+i))^4=...

`((1+i)/(1-i))^4+((1-i)/(1+i))^4=`

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SIA PUBLICATION-COMPLEX NUMBERS AND DE MOIVRE'S THEOREM-Problems
  1. The least positive integer n for which (1+i)^(n)=(1-i)^(n). is

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  2. If x=p+q,y=pomega+q omega^(2) and z=p omega^(2)+q omega, where omega i...

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  3. ((1+i)/(1-i))^4+((1-i)/(1+i))^4=

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  4. If a complex number z satisfies |z|^(2)+1=|z^(2)-1|, then the locus of...

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  5. ((1+i)x-i)/(2+i)+((1+2i)y+i)/(2-i)=1rArr(x,y)=

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  6. If a,b,c,d inRR are such that a^2+b^2=4 and c^2+d^2=2 and if (a+ib)^2...

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  7. If alpha is a non real root of the equation x^(6)-1=0 then (alpha^(2)+...

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  8. Let z=a-i/2,a inRR " Then "|i+z|^2-|i-z|^2=

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  9. The locus of the complex number z such that arg ((z-2)/(z+2))=pi/3 is ...

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  10. ((1+i)^2011)/(1-i)^2009=

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  11. z=1+isqrt(3)rArr|Arg z|+|Argbarz|=

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  12. If omega is a complex cube root of unity, then (x+1)(x+omega)(x-omega-...

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  13. The locus of z satisfying the |(x+2i)/(2z+i)| lt 1, inequality where z...

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  14. The points in the set {zinC: Arg " ((z-2)/(Z-6i))=pi/2} lie on the cu...

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  15. If omega is a complex cube root of unity, then sin[(omega^(10)+omega^(...

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  16. If m(1), m(2), m(3) and m(4) respectively denote the moduli of the co...

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  17. The locus of the point z=x+iy satisfying |(z-2i)/(z+2i)|=1 is

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  18. The equation of the locus of 2 such that |(z-i)/(z+i)|=2, where z = x ...

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  19. If alpha1,alpha2,alpha3 respectively denote the moduli of the complex ...

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  20. sum(n=0)^oo((2i)/3)^n=

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