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Write the following in the form x+iy: ...

Write the following in the form x+iy:
(i) `i+i^(2)+i^(3)+i^(4)`
(ii) `i^(4)+i^(8)+i^(12)+i^(16)`
(iii) `i+i^(5)+i^(9)+i^(13)`
(iv) `i^(9)+i^(10)+i^(11)+i^(12)`.

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The correct Answer is:
(i) 0+0i, (ii) 4+0i, (iii) 0+4i, (iv) 0+0i.
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MODERN PUBLICATION-COMPLEX NUMBERS-Exercise 5 (e) Short Answer Type Questions
  1. Write the following in the form x+iy: (i) (2i)^(3) (ii) i^(-35) ...

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  2. Express the following in the form a+i b : (-5i)(1/8i)

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  3. Write the following in the form x+iy: (i) i+i^(2)+i^(3)+i^(4) (ii)...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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