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If (x+iy)^(1/3)=a+ib, where a,b,x, y in ...

If `(x+iy)^(1/3)=a+ib`, where a,b,x, y in R, show that `x/a-y/b=-2(a^2+b^2)`.

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JBD PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-EXAMPLE
  1. If z=x+iy and |z+a|=3|z-a|, show that 2(x^2+y^2)=5ax-2a^2.

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  2. Solve 2x^2+x+1=0

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  3. Solve the following equation : 2x^2-(3 +7i)x + (9i-3)=0.

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  4. Find the modulus and argument of the complex number (1+2 i)/(1- 3i)

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  5. If (x + iy)^3 = u + iv, then show that u/x +v/y = 4(x^2 - y^2)

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  6. If x-iy= sqrt((a-ib)/(c-id)) prove that (x^2+y^2)^2= (a^2+b^2)/(c^2+d^...

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  7. If (a+ib)(c+id)(e+if)(g+ih)=A+iB, then show that: (a^2+b^2)(c^2+d^2)(e...

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  8. Find the square root of i.

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  9. Find the square root of 1+i.

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  10. Find the squre root of 1+2sqrt(6)i.

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  11. Convert each of the complex numbers given below in the polar form. Als...

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  12. Convert each of the complex numbers given below in the polar form. Als...

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  13. Convert each of the complex number -16/(1+isqrt3) into polar form. Als...

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  14. If ((1+i)/(1-i))^3-((1-i)/(1+i))^3=x+iy, then find (x,y)

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  15. If (x+iy)^(1/3)=a+ib, where a,b,x, y in R, show that x/a-y/b=-2(a^2+b^...

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  16. If z=x+iy and |z|=1, show that the complex number z1=(z-1)/(z+1) is pu...

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  17. Convert z= (i-1)/(cos frac (pi)(3)+i sin frac (pi)(3)) in polar form.

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  18. If the imaginary part of (2z+1)/(iz+1) is -2, then the locus of the po...

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  19. If the complex number z1 and z2be such that arg(z1)-arg(z2)=0, then sh...

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  20. Solve the system of equations Re(z^2)=0, |z|=2.

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