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If omega and omega^2 be the imaginary cu...

If `omega` and `omega^2` be the imaginary cube roots of unity then find the value of `(3+3omega+5omega^2)^6-(2+6omega+2omega^2)^3`

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PATHFINDER-COMPLEX NUMBERS-QUESTION BANK
  1. The value of (cos(pi/10)+isin(pi/10))(cos((2pi)/10)+isin((2pi)/10))...

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  2. If (a+i)^2/(2a-1)=p+iq then find the values of (p^2+q^2)

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  3. If omega and omega^2 be the imaginary cube roots of unity then find th...

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  4. Value of i^(n)+i^(n+1)+i^(n+2)+i^(n+3)("when" i=sqrt(-1))-

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  5. If (1+i)(2+i)(3+i)………(n+i)=a+ib then show that 2.5.10……….(n^2+1)=a^2+...

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  6. Find the least possible integral value of n so that ((1+i)/(1-i))^n' i...

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  7. Find the amplitude of (sqrt3+i)

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  8. Find the value of sqrt([-3+sqrt(({-3+sqrt(-3+... "to infinity"}})]])

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  9. Express 1/(1-i)^3 in the form A+iB

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  10. Find the square root of (i)

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  11. Show that x^3-1=(x-1)(x-omega)(x-omega^2)

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  12. Find 4th roots of 1

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  13. Express each of the following expressions as the sum of two squares: (...

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  14. Ifabs(z)gt1 then find the position of the complex no. of z in argand p...

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  15. If abs(z+2)+abs(z-2)le6 then find the maximum value of abs(z)

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  16. Ifz^2+abs(z)^2=0 then find the imaginary value of z

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  17. Show that in argand plane the complex number (1+4i),(2+7i)and (3+10i) ...

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

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

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

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