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Prove that: x^4+4=(x+1+i)(x+1-i)(x-1+i)(...

Prove that: `x^4+4=(x+1+i)(x+1-i)(x-1+i)(x-1-i)`.

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Given, R.H.S
`=(x+1+i)(x+1−i)(x−1+i)(x−1−i)`
`=[(x+1)^2-i^2] [(x-1)^2-i^2]`
`=(x^2+2x+1+1)(x^2-2x+1+1)`
...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. If (1+i)(1+2i)(1+3i)(1+n i)=(x+i y) , Show that 2.5.10 ..... (1+n^2)=x...

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  2. Find the value of x^3+7x^2-x+1,\ w h e n\ x=1+2idot

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  3. Prove that: x^4+4=(x+1+i)(x+1-i)(x-1+i)(x-1-i).

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  4. Show that a real value of x\ will satisfy the equation (1-ix)/(1+ix)=...

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  5. If alphaand betaare different complex numbers with |beta|=1,then fin...

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  6. Find non zero integral solutions of |1-i|^x=2^xdot

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  7. Express the following complex numbers in the standard form a+i b :(1+i...

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  8. Express the following complex numbers in the standard form a+i b :1/((...

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  9. Express the following complex numbers in the standard form a+i b :((2+...

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  10. Express the following complex numbers in the standard form a+i b :(1+2...

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  11. Express the following complex numbers in the standard form a+i b :(1/(...

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  12. Express the following complex numbers in the standard form a+i b :(3+2...

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  13. Express the following complex numbers in the standard form a+i b :(1-i...

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  14. Express the following complex numbers in the standard form a+i b :((1+...

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  15. Express the following complex numbers in the standard form a+i b :(3-4...

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  16. Express the following complex numbers in the standard form a+i b :(5+s...

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  17. Find the real values of x\ a n d\ y ,\ if:(x+i y)(2-3i)=4+i

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  18. Find the real values of x\ a n d\ y ,\ if:((1+i)x-2i)/(3+i)+((2-3i)y+i...

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  19. Find the real values of x\ a n d\ y ,\ if:(3x-2iy)(2+i)^2=10(1+i)

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  20. Find the real values of x\ a n d\ y ,\ if:(1+i)(x+i y)=2-5i

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