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If (1+i)(1+2i)(1+3i)...(1+n i)=a+i b , t...

If `(1+i)(1+2i)(1+3i)...(1+n i)=a+i b ,` then the value of; `2. 5. 10. 17... (1+n^2\ )` will be `(a)`. `a-i b` `(b)`. `a^2-b^2` `(c)`. `a^2+b^2` `(d)`. none of these

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RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. If z=(-2)/(1+isqrt(3)) , then the value of "arg"(z) is a. pi b. pi/4 c...

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

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  3. 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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  4. 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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  5. The principal value of the amplitude of (1+i) is A. pi B. pi/(12) C...

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

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

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  8. If a=1+i , then a^2 equals A. 1-i B. 2i C. (1+i)(1-i) D. (i-1)

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  9. If (x+i y)^(1//3)=a+i b ,\ then\ x/a+y/b is a. 0 b. 1 c. -1 d. none o...

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  10. (sqrt(-2))(sqrt(-3)) is equal to A. sqrt(6) B. -sqrt(6) C. isqrt(6)...

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  11. The argument of (1-isqrt(3))/(1+isqrt(3)) is a. 60^@ b. 120^@ c. 210^@...

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  12. If z=((1+i)/(1-i)), then z^4 equals to

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  13. If z=(1+2i)/(1-(1-i)^2), then arg(z) equals a. 0 b. pi/2 c. pi ...

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  14. If z=1/((2+3i)^2), then |z| is (a). 1/13 (b) . 1/5 (c) . 1...

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  15. If z=1/((1-i)(2+3i)), then |z| is (a). 1 (b). 1/sqrt(26) (c). 5...

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  16. If z=1-costheta+isintheta,\ t h e n\ |z| is equal to a. 2sin(theta/2)...

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  17. If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2 is: (a). 0 (b). 1 (c). 1...

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  18. If z=1/(1-cos theta-i sin theta), then Re(z) is a. 0 b. 1/2 c. c...

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  19. If x+i y=(3+5i)/(7-6i), then y is A. 9/85 B. -9/(85) C. (53)/(85) ...

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  20. The amplitude of 1/i is equal to a. 0 b. pi/2 c. -pi/2 d. pi

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