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For |z-1|=1, show that tan{[a r g(z-1)]/...

For `|z-1|=1,` show that `tan{[a r g(z-1)]//2}-(2i//z)=-idot`

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VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 2
  1. Solve for z : z^2-(3-2i)z=(5i-5)dot

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  2. Find number of values of complex numbers omega satisfying the system o...

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  3. For |z-1|=1, show that tan{[a r g(z-1)]//2}-(2i//z)=-idot

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  4. If nge3and1,alpha(1),alpha(2),.......,alpha(n-1) are nth roots of unit...

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  5. Let |z|=2and w=(z+1)/(z-1),where z ,w , in C (where C is the set of c...

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  6. If z=x+i y is a complex number with x ,y in Qa n d|z|=1, then show th...

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  7. If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies...

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  8. Given z=f(x)+ig(x) where f,g:(0,1) to (0,1) are real valued functions....

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  9. Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...

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  10. If m and x are two real number s and i=sqrt(-1), prove that e^(2mico...

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  11. Find the range of real number alpha for which the equation z + al...

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  12. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

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  13. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4a n d ...

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  14. If the equation z^4+a1z^3+a2z^2+a3z+a4=0 where a1,a2,a3,a4 are real co...

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  15. The value of the expression 2(1+(1)/(omega))(1+(1)/(omega^(2)))+3(2+(1...

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  16. If z=ilog(e)(2-sqrt(3)),"where"i=sqrt(-1) then the cos z is equal to

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  17. If z satisfies |z+1| lt |z-2|, then w=3z+2+i

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  18. For any two complex numbers z1\ a n d\ z2 and any two real numbers a ,...

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  19. If w=cos""(pi)/(n)+isin""(pi)/(n) then value of 1+w+w^(2)+.......+w^(n...

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  20. Find the sum 1xx(2-omega)xx(2-omega^(2))+2xx(-3-omega)xx(3-omega^(2))+...

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