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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 number `i=sqrt(-1)`:
Prove that: `[(sqrt(7)+isqrt(3))/(sqrt(7)-isqrt(3))+(sqrt(7)-isqrt(3))/(sqrt(7)+isqrt(3))]` is real.

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(sqrt(7)+sqrt(3))/(sqrt(7)-sqrt(3))-(sqrt(7)-sqrt(3))/(sqrt(7)+sqrt(3))

sqrt(3)(sqrt(7)-sqrt(3))

(sqrt(7)-sqrt(5))^3 - (sqrt(7)+sqrt(5))^3

Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : (i) (-5+3i)(8-7i) (ii) (-sqrt(3)+sqrt(-2))(2sqrt(3)-i) (iii) (sqrt(2)-sqrt(3)i)^(2)

Perform the following by the indicated operations. Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : Simply: (i) (sqrt(5)+7i)(sqrt(5)-7i)^(3) (ii) (1+i)(2+3i)(3+4i)(4+5i) (iii) (1+i^(2))+i^(4)+i^(6) .

(3+sqrt(7))/(3-sqrt(7))

sqrt(7+4sqrt3) - sqrt(7-4sqrt3) =

sqrt(2)+sqrt(3)+sqrt(7)-(1)/(sqrt(2)+sqrt(3)+sqrt(7))=?

Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : (i) 3i^(3)(15i^(6)) (ii) (2+7i)^(3) (iii) ((1)/(2)+2i)^(3)

smplify (7+sqrt(3))/(7-sqrt(3))+(7-sqrt(3))/(7+sqrt(3))

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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