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If |z|=1, prove that (z-1)/(z+1) (z ne -...

If |z|=1, prove that `(z-1)/(z+1) (z ne -1)` is purely imaginary number. What will you conclude if z=1?

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MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
  1. Find the non-zero integral solutions of |1-i|^x=2^x.

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

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

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

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

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

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

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

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

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

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  11. Express 1+isqrt3 in polar form.

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

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

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  14. Find the absolute values and arguments of following complex numbers : ...

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  15. Find the absolute values and arguments of following complex numbers : ...

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  16. Find the absolute values and arguments of following complex numbers : ...

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  17. If two complex numbers z1,z2 are such that |z1|= |z2|, is it then nece...

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  18. Give the following in polar form : sin 120^@ -i cos 120^@.

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  19. Give the following in polar form : [2(cos 210^@ + i sin 210^@)] [4(c...

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  20. Give the following in polar form : [3(cos 225^@ + i sin 225^@)] [6(c...

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