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If u+iv=(2+i)/(z+3) and z=x+iy find u, v...

If `u+iv=(2+i)/(z+3) and z=x+iy` find u, v

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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-COMPLEX NUMBERS-EXERCISE -1 (B)
  1. Find the square root of the following complex number: -8-6i

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  2. Find a square root for the complex numbers. (3+4i)

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  3. Find a square root for the complex numbers. (-47+i8 sqrt(3))

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  4. Find the multiplicative inverse of the complex numbers. sqrt(5)+3i

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  5. Find the multiplicative inverse of the complex numbers. -i

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  6. Find the multiplicative inverse of the complex numbers. i^(-35)

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  7. If (a+ib)^(2)=x+iy, find x^(2)+y^(2)

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  8. If x+iy=3/(2+costheta +i sin theta), then show that x^2+y^2=4x-3

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  9. If x+iy=(1)/(1+ cos theta+ isin theta), show that 4x^(2)-1=0

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  10. If u+iv=(2+i)/(z+3) and z=x+iy find u, v

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  11. If z=3-5i Show that z^(3)-10z^(2)+58z-136=0

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  12. If z=2-isqrt(7), then show that 3z^(3)-4z^(2)+z+88=0

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  13. Show that (2-i)/((1-2i)^(2)) and ((-2-11 i)/(25)) are conjugate to eac...

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  14. (x+iy)^(1/3) =(a+ib) then prove that (x/a+y/b)=4(a^2-b^2)

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  15. Write ((a+ib)/(a-ib))^(2)-((a-ib)/(a+ib))^(2) in the fom of x+iy

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  16. If x and y are real numbers of such that ((1+i)x-2i)/(3+i)+((2-3i)y+i...

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  17. Find the least positive integer n foe which ((1+i)/(1-i))^(n)=1.

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  18. If ((1+i)/(1-i))^3-((1-i)/(1+i))^3=x+i y ,\ fin d\ (x , y)

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  19. Find the value of theta if (3+2isintheta)//(1-2isintheta) is purely re...

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  20. Find the real values of x and y if (x-1)/(3+1)+(y-1)/(3-i)=i

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