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

If `z_1 = 5 + 7i` and `z_2= 7 - 9i`,verify : `|z_2-z_1| > |z_2|- |z_1|`.

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If z_1 = 5 + 7i and z_2= 7 - 9i ,verify : |-z_1|=|z_1| .

If z_1 = 5 + 7i and z_2= 7 - 9i ,verify : |z_1 z_2|=|z_1| |z_2| .

If z_1 = 5 + 7i and z_2= 7 - 9i ,verify : |z_1^2|=|z_1|^2 .

If z_1 = 5 + 7i and z_2= 7 - 9i ,verify : |z_1+z_2| <|z_1|+ |z_2| .

If z_1 = 5 + 7i and z_2= 7 - 9i ,verify : |z_1/z_2|= (|z_1|)/ (|z_2|) .

Let z_1=2- 3i and z_2= 5 + 12i , verify that : |z_2-z_1| >|z_2|-|z_1| .

If z_1 = 3 + 4i and z_2=12 -5i , verify : |-z_1|=|z_1| .

If z_1 = 3 + 4i and z_2=12 -5i , verify : |z_1+z_2|<|z_1|+ |z_2| .

If z_1 = 3 + 4i and z_2=12 -5i , verify : |z_1 z_2|= |z_1| |z_2| .

Let z_1=2- 3i and z_2= 5 + 12i , verify that : |z_1+z_2| <|z_1|+|z_2| .

MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
  1. If z1 = 5 + 7i and z2= 7 - 9i,verify : |z1^2|=|z1|^2.

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Convert the given complex number in polar form -1 + i

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

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  16. Find the given complex number in polar form : -3

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  17. Convert the complex numbers given below in the polar form: sqrt3 + i

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  18. Express 1+isqrt3 in polar form.

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  19. Convert the following complex numbers in polar form : i.

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  20. Convert the following in the polar form: (1+ 3i)/(1-2i)

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