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Let z1=2- 3i and z2= 5 + 12i, verify tha...

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

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MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
  1. For any complex number z, prove that : -|z| leRe (z) le |z|.

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  2. For any complex number z, prove that : -|z| leIm (z) le |z|.

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  3. Let z1=2- 3i and z2= 5 + 12i, verify that : |z1+z2| <|z1|+|z2|.

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  4. Let z1=2- 3i and z2= 5 + 12i, verify that : |z2-z1| >|z2|-|z1|.

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  5. In the following perform the indicated operations and write the result...

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  6. In the following perform the indicated operations and write the result...

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  7. In the following perform the indicated operations and write the result...

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  8. In the following perform the indicated operations and write the result...

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  9. In the following perform the indicated operations and write the result...

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  10. Express the complex number given below in the form a + ib:- (1 -i)-(-1...

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  11. Express the complex number given below in the form a + ib:- 3(7 + i7) ...

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  12. In the following perform the indicated operations and write the result...

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  13. In the following perform the indicated operations and write the result...

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  14. In the following perform the indicated operations and write the result...

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  15. In the following perform the indicated operations and write the result...

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  16. Express the complex number given below in the form a + ib:- [(1/3+i 7/...

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  17. In the following perform the indicated operations and write the result...

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  18. In the following perform the indicated operations and write the result...

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  19. Find the sum of : 2/3+5/3i, -2/3 i and (-5)/4-i.

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  20. Write the following in the form x + iy : (2i)^3.

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