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If z=x+iy and |z+a|=3|z-a|, show that 2(...

If z=x+iy and |z+a|=3|z-a|, show that `2(x^2+y^2)=5ax-2a^2`.

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JBD PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-EXAMPLE
  1. Find the modulus of the following complex numbers: (2+3i)^2/(1-3i)

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  2. Find the number of non-zero integral solutions of the equation |1- i|^...

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  3. If z=x+iy and |z+a|=3|z-a|, show that 2(x^2+y^2)=5ax-2a^2.

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

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

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

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

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  8. 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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  9. 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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  10. Find the square root of i.

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  11. Find the square root of 1+i.

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

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

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

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

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

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

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

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

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