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If x+i y=sqrt((a+i b)/(c+i d)) prove tha...

If `x+i y=sqrt((a+i b)/(c+i d))` prove that `(x^2+y^2)^2=(a^2+b^2)/(c^2+d^2)`

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RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. Find the multiplicative inverse of the following complex number: (2+sq...

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  2. If a+i b=((x+i)^2)/(2x^2+1), prove that a^2+b^2=((x^2+1)^2)/((2x^2+1)^...

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  3. If x+i y=sqrt((a+i b)/(c+i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d...

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  4. Find the least positive value of n if ((1+i)/(1-i))^n=1.

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  5. Find real theta such that (3+2i\ sintheta)/(1-2i\ sintheta) is purely ...

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

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

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

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  10. If alpha an d beta are different complex numbers with |beta|=1,then ...

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

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

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

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

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

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

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

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

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

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

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