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If x=a+b ,y=aomega+bomega^2, z=aomega^2+...

If x=a+b ,`y=aomega+bomega^2`, `z=aomega^2+bomega` then show that ,`x^3+y^3+z^3=3(a^3+b^3)`

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PATHFINDER-COMPLEX NUMBERS-QUESTION BANK
  1. Show that in argand plane the complex number (1+4i),(2+7i)and (3+10i) ...

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  2. z1 and z2 are two different complex nos where z1ne0 z2ne0 prove that (...

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  3. If x=a+b ,y=aomega+bomega^2, z=aomega^2+bomega then show that ,x^3+y^3...

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  4. Find the modulus and amplitude of the complex nos (1+cosalpha+isinalph...

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  5. Express the complex nos (1+7i)/(2-i)^2 in polar form

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  6. Factorise a^3+b^3+c^3-3abc

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  7. Find the square roots : x-isqrt(x^(4)+x^(2)+1)

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  8. If omega is the imaginary cube root of 1 then prove that (a+bomega+com...

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  9. If y=sqrt(x^2+6x+8) then show that one of the value of sqrt(1+iy)+sqrt...

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  10. If x=cosalpha+isinalpha and 1+sqrt(1-y^2)=ny then show that y/2n(1+nx)...

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  11. If a=1/2(5-isqrt3) then find the value of a^3-6a^2+12a-8

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  12. Show that complex numbers (2+i3), (2-i3), (3-i2), (3+i2) are concyclic...

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  13. If in argand plane the vertices A,B,C of an isoceles triangle are rep...

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  14. If z1,z2,z3 are three complex number then prove that z1Im(barz2.z3)+z2...

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  15. Prove that (1-omega^2)(1-omega^2+omega^4)(1-omega^4+omega^8)………..to 2n...

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  16. If x-iy = sqrt((a+ib)/(c-id)), prove that (x^(2) + y^(2))^(2) = (a^(2)...

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  17. If z be complex no. and (z-1)/(z+1) be purely imaginary show that z li...

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  18. z1 and z2 be two complex no. then prove that abs(z1+z2)^2+abs(z1-z2)^2...

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  19. If z=3/(2+costheta+isintheta) then show that z lies on a circle in the...

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  20. If a=cosalpha+isinalpha , b=cosbeta+isinbeta , c=cosgamma+isingamma an...

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