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Find the least possible integral value of n so that `((1+i)/(1-i))^n' is real

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PATHFINDER-COMPLEX NUMBERS-QUESTION BANK
  1. Value of i^(n)+i^(n+1)+i^(n+2)+i^(n+3)("when" i=sqrt(-1))-

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

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  4. Find the amplitude of (sqrt3+i)

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

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

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  7. Find the square root of (i)

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

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  9. Find 4th roots of 1

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

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

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

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

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

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

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

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

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

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

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

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