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Perform the following by the indicated o...

Perform the following by the indicated operations. Express the result in the form x + iy,where x, y are real numbers `i = sqrt(-1)` :
`1/i^7`.

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MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
  1. Perform the following by the indicated operations. Express the result ...

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  2. Perform the following by the indicated operations. Express the result ...

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  3. Perform the following by the indicated operations. Express the result ...

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  4. Perform the following by the indicated operations. Express the result ...

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  5. Perform the following by the indicated operations. Express the result ...

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  6. Perform the following by the indicated operations. Express the result ...

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  7. Simplify : (sqrt5+7i)(sqrt5-7i)^3.

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  8. Simplify : (1+i)(2+3i)(3+4i)(4+5i).

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  9. Simplify : (1+i^2) +i^4+i^6.

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  10. Prove that [(sqrt7+i sqrt3)/(sqrt7-i sqrt3)+(sqrt7-i sqrt3)/ (sqrt7+i ...

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  11. Compute : sqrt(-49)(2+sqrt(-9)).

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  12. Compute : [2+ sqrt(-25)]-[3-sqrt(-16)]+[1-sqrt(-9)].

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  13. Find theta such that (3+2i sin theta)/(1-2i sin theta) is purely real.

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  14. Write the conjugates of the following : 3+i.

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  15. Write the conjugates of the following : 3-i.

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  16. Write the conjugates of the following : -sqrt5-sqrt7 i.

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  17. Write the conjugates of the following : -sqrt5 i.

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  18. Write the conjugates of the following : 4/5.

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  19. Write the conjugates of the following : 49-i/7.

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  20. Write the conjugates of the following : (1-i)/(1+i).

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