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Prove that 1+ i^10+i^20+i^30 is a real n...

Prove that `1+ i^10+i^20+i^30` is a real number.

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MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
  1. Find the value of [i^19+(1/i)^25]^2

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  2. Prove that : 2i^2+6i^3+3i^16-6i^19+4i^25=1+4i.

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  3. Prove that 1+ i^10+i^20+i^30 is a real number.

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  4. Show that (-sqrt(-1))^(4n+3)=i, where n is a positive integer.

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  5. Write the following as complex numbers : sqrt(-27).

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  6. Write the following as complex numbers : sqrt x, (x > 0).

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  7. Write the following as complex numbers : 1+sqrt (-1).

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  8. Write the following as complex numbers : 4-sqrt (-5).

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  9. Write the following as complex numbers : sqrt 3/2- (sqrt (-2))/7.

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  10. Write the real and imaginary parts of the following complex numbers : ...

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  11. Write the real and imaginary parts of the following complex numbers : ...

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  12. Write the real and imaginary parts of the following complex numbers : ...

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  13. Write the real and imaginary parts of the following complex numbers : ...

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  14. Write the real and imaginary parts of the following complex numbers : ...

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  15. Write the real and imaginary parts of the following complex numbers : ...

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  16. Write the real and imaginary parts of the following complex numbers : ...

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  17. Write the real and imaginary parts of the following complex numbers : ...

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  18. Find real numbers x and y such that 3x +2iy-ix+5y =7 +5i.

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  19. Find x and y such that 2x + 4iy and 2i represent the same complex numb...

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  20. Find x and y, if (3y - 2) +i(7-2x) = 0.

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