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For any two complex numbers z1\ a n d\ z...

For any two complex numbers `z_1\ a n d\ z_2` and any two real numbers `a ,\ b` find the value of `|a z_1-b z_2|^2+|a z_2+b z_1|^2dot`

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RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. Write the value of a r g(z)+a r g( barz ) .

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  2. If |z+4|lt=3 then find the greatest and least values of |z+1|dot

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  3. For any two complex numbers z1\ a n d\ z2 and any two real numbers a ,...

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  4. If n in NN ,then find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3).

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  5. Find the real value of a for which 3i^3-2a i^2+(1-a)i+5 is real.

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  6. If |z|=2 and arg (z)=pi/4 , find z.

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  7. Write the argument of (1+isqrt(3))(1+i)(costheta+isintheta).

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  8. The value of (1+i)(1+i^2)(1+i^3)(1+i^4) is a. 2 b. 0 c. 1 d. i

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  9. If (3+2i sintheta)/(1-2i sintheta) is a real number and 0lt theta lt 2...

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  10. If sqrt(a+i b)=x+i y ,\ then possible value of sqrt(a-i b) is a. x^2+...

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  11. If z=cos(pi/4)+isin(pi/6) , then a. |z|=1, arg(z)=\ pi/4 b. |z|=1, arg...

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  12. The polar form of (i^(25))^3 is a. cos(pi/2)+isin(pi/2) b. cospi+i\ si...

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  13. If i^2=-1, then the sum i+i^2+i^3+... upto 1000 terms is equal to a. 1...

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  14. If z=(-2)/(1+isqrt(3)) , then the value of "arg"(z) is a. pi b. pi/4 c...

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  15. If a=costheta+isintheta, then (1+a)/(1-a) is: (a). cot(theta/2) (b). ...

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  16. If (1+i)(1+2i)(1+3i)...(1+n i)=a+i b , then the value of; 2. 5. 10. 17...

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  17. If ((a^2+1)^2)/(2a-i)=x+i y , then x^2+y^2 is equal to a. ((a^2+1)^4)/...

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  18. The principal value of the amplitude of (1+i) is A. pi B. pi/(12) C...

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  19. The least positive integer n such that ((2i)/(1+i))^n is a positive in...

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  20. If z is a non zero complex, number then |(|barz |^2)/(z barz )| is eq...

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