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Find the integral solutions of the follo...

Find the integral solutions of the following equation: `(1-i)^x=(1+i)^x`

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The integral solution of (1-i)^x=2^x is

A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. Sum of common roots of the equations z^(3) + 2z^(2) + 2z + 1 =0 and z...

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  2. Solve: "^8C0x^8+^8C2x^6+^8C4x^4+^8C6x^2+1=0.

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  3. Find the integral solutions of the following equation: (1-i)^x=(1+i)^x

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  4. Solve (1+i)^x = 2^x where x is an integer ne 0.

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  5. If x^2-2xcos theta+1=0, then the value of x^(2n)-2x^n cosntheta+1, n ...

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  6. If 2cos A = x+1/x , 2cosbeta=y+1/y then show that 2cos(A-B) =x/y+y/x.

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  7. If xn =cos ((pi)/(2^(n)))+isin((pi)/(2^(n)))Prove that x1 x2…..xoo=-1

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  8. If z1, z2 be the complex numbers satisfying x^2+4=2x, prove that z1^n+...

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  9. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)++a(n...

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  10. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)++a(n...

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  11. If z^7+1 =0 then cos(pi/7) cos((3pi)/7) cos((5pi)/7) is (A) 1/8 ...

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  12. Hence deduce that cos(pi)/(9)cos(2 pi)/(9)cos(3 pi)/(9)cos(4 pi)/(9)=(...

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  13. (2+omega+omega^2)^3+(1+omega-omega^2)^3=(1-3omega+omega^2)^4=1

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  14. (i) If alpha,beta be the imaginary cube root of unity, then show that ...

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  15. If x=a+b,y=aomega+bomega^2 nd z=omega^2+bomega, prove that x^3+y^3+z^3...

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  16. If x = a + b, y= aw + bw^2 and z = aw^2 + bw, where w is an imaginary ...

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  17. Prove that ((i+sqrt3)/2)^100+((i-sqrt3)/2)^100+1=0.

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  18. What is the value of ((i+sqrt3)/(-i+sqrt3))^(200)+((i-sqrt3)/(i+sqrt3)...

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  19. Prove that sqrt(-1-sqrt(-1-sqrt1-… prop=w or w^2 .

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  20. Resolve into the linear factor: a^3+b^3

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