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If (x+i y)^5=p+i q , then prove that (y+...

If `(x+i y)^5=p+i q ,` then prove that `(y+i x)^5=q+i pdot`

A

q +ip

B

p-iq

C

q-ip

D

`-p-ip`

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The correct Answer is:
A
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ML KHANNA-COMPLEX NUMBERS -Problem Set (2) (M.C.Q)
  1. If ( sqrt( 3) + i) ^(10) = a + ib then, a and b are respectively

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  2. The solution of the equation (1 + i sqrt(3))^(x) = 2^(x) are in

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  3. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

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  4. Sum of sixth power of the roots of the equation t^(2) - 2t + 4 = 0 i...

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  5. (1 + i) ^(8) + (1 - i) ^(8) =

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  6. If [ (sqrt(3) // 2 + (1 //2)i)/(sqrt(3) // 2 - (1//2)i)] ^(120) = a +...

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  7. (-64)^(1//4) is equal to-

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  8. The points representing 3 sqrt(sqrt""5 + isqrt""3) lie

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  9. Given z is a complex number with modulus 1. Then the equation ((1 +...

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  10. If z=((sqrt(3))/2+i/2)^5+((sqrt(3))/2-i/2)^5 , then prove that I m(z)=...

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  11. ((cos theta + i sin theta)^(4))/( (sin theta + i cos theta)^(5)) is eq...

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  12. If a^(2)+b^(2)=1, prove that (1+b+ia)/(1+b-ia)=b+ia.

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  13. If z(1+a)=b+i ca n da^2+b^2+c^2=1, then [(1+i z)//(1-i z)= (a+i b)/(1...

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  14. The value of sum (k = 1)^(6) ( sin "" ( 2 pi k)/( 7) - i cos "" ( 2 p...

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  15. The value of sum (k = 0) ^(10) ( sin "" ( 2 k pi)/(11) + i cos "" (2 ...

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  16. [(1 + sin "" (pi)/( 8) + i cos "" (pi)/( 8))/( 1 + sin "" (pi)/( 8) - ...

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  17. If [(1 + cos theta + i sin theta)/( sin theta + i (1 + cos theta))] ^...

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  18. The value of 1 + sum (k = 0)^( 12) { cos "" (( 2 k + 1) pi)/( 13) + i...

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  19. If z(r) = cos ( pi // 2^(r)) + i sin ( pi // 2 ^(r)) r = 1, 2, . . . ...

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  20. If zr=cos(pi/(3r))+isin(pi/(3r)),r=1,2,3, , prove that z1z2z3 zoo=idot

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