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Prove that: (i) z=overline(z) iff z is...

Prove that:
(i) `z=overline(z)` iff z is real
(ii) `z=-overline(z)` iff z is either zero or purely imaginary.

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MODERN PUBLICATION-COMPLEX NUMBERS-Exercise 5 (e) Short Answer Type Questions
  1. Express the result in the form x+iy, where x,y are real number i=sqrt(...

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  2. Express the result in the form x+iy, where x,y are real number i=sqrt(...

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  3. Express the result in the form x+iy, where x,y are real number i=sqrt(...

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  4. Express the result in the form x+iy, where x,y are real number i=sqrt(...

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  5. Express the result in the form x+iy, where x,y are real number i=sqrt(...

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

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

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  8. Compute: (i) sqrt(-49)(2+sqrt(-9)) (ii) [2+sqrt(-25)]-[3-sqrt(-16)]+...

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  9. Find real q such that (3+2isintheta)/(1-2isintheta) is purely real.

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  10. (a) Write the conjugates of the following: (i) 3+i (ii) 3-i (iii...

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  11. Find the reciprocal of : (i) 7+sqrt(7)i (ii) i-5.

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  12. Prove that: (i) z=overline(z) iff z is real (ii) z=-overline(z) if...

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  13. Prove that: R(e)z=(z+overline(z))/(2),I(m)z=(z-overline(z))/(2i)

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  14. Prove that: (i) the sum of a complex number and its conjugate is real ...

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  15. Give an example to show that subtraction of complex number is not comm...

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  16. Find the sum and product of the complex numbers -sqrt(3)+sqrt(-2) and ...

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  17. If z(1),z(2) are respectively 1-i,-2+4i, find I(m){(z(1)z(2))/(z(1))}.

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  18. Finid the vlues of x and y if: (i) (x+iy)(1+i)=1-i (ii) ((1+i)x-2i...

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  19. If 1+4sqrt(3)i=(1+ib)^(2), prove that: a^(2)-b^(2)=1 and ab=2sqrt(3)...

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  20. Show that if a,b,c,d in R, overline((a+ib)(c+id))=(a-ib)(c-id).

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