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Prove that [4+ 3 sqrt(- 20)]^(1//2) +[4-...

Prove that `[4+ 3 sqrt(- 20)]^(1//2) +[4-3 sqrt(- 20)]^(1//2)= 6`.

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MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
  1. Find the square roots of the following : 4+6 sqrt(-5).

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  2. Find the square roots of the following : -2+2 sqrt3 i.

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  3. Prove that [4+ 3 sqrt(- 20)]^(1//2) +[4-3 sqrt(- 20)]^(1//2)= 6.

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  4. Evaluate : x^2+4x+7 when x =-2+ sqrt(-3).

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  5. Evaluate : 2x^3-9x^2-10x+13 when x =3+ sqrt(5).

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  6. Evaluate : x^4-3x^3+3x^2+99x-95 when x =3-4i.

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  7. If z1 = 5 + 7i and z2= 7 - 9i,verify : |-z1|=|z1|.

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  8. If z1 = 5 + 7i and z2= 7 - 9i,verify : |z1^2|=|z1|^2.

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  9. If z1 = 5 + 7i and z2= 7 - 9i,verify : |z1+z2| <|z1|+ |z2|.

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  10. If z1 = 5 + 7i and z2= 7 - 9i,verify : |z2-z1| > |z2|- |z1|.

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  11. If z1 = 5 + 7i and z2= 7 - 9i,verify : |z1 z2|=|z1| |z2|.

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  12. If z1 = 5 + 7i and z2= 7 - 9i,verify : |z1/z2|= (|z1|)/ (|z2|).

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  13. If z is any complex number, prove that : |z|^2= |z^2|.

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  14. If iz^3+z^2-z+i = 0, then show that |z|=1.

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  15. Find the non-zero integral solutions of |1-i|^x=2^x.

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  16. If |z1|=|z2|= ...... |zn|=1, prove that : |z1+z2+ ........ zn|= |1/z1...

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  17. If |z|=1, prove that (z-1)/(z+1) (z ne -1) is purely imaginary number....

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  18. If z1 and z2 (ne 0) are two complex numbers, prove that : |z1 z2|= |z1...

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  19. If z1 and z2 (ne 0) are two complex numbers, prove that : |z1/z2|= (|z...

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  20. Convert the following complex numbers in polar form : 1-i .

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