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For some integer k, i^(4k)+i^(4k+1)+i^(4...

For some integer `k, i^(4k)+i^(4k+1)+i^(4k+2)+i^(4k+3)` = ..........

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The distance between the line bar r = 2 hat i - 2 hat j + 3 hat k + lambda(hat i - hat j + 4 hat k) and the plane bar r. (hat i + 5 hat j + hat k) = 5 is..........

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For any integer k , let alpha_k=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt(-1)dot Value of the expression (sumk=1 to 12|alpha_(k+1)-alpha_k|)/(sumk=1 to 3|alpha_(4k-1)-alpha_(4k-2)|) is

The angle between the line bar r = (2 hat i - hat j + hat k) + lambda( - hat i + hat j + hat k) and the plane bar. (3 hat i + 2 hat j - hat k) = 4 is...............

Find the values of k for which the line (k-3) x-(4-k^2) y+k^2 -7k+6=0 is (i) Parallel to the x-axis Line (k-3) x-(4-k^(2) ) y+k^(2) -7k+6=0 .

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KUMAR PRAKASHAN-OBJECTIVE SECTION AS PER NEW PAPER SCHEME -Complex numbers and Quadratic Equations (Fill in the Blanks)
  1. For some integer k, i^(4k)+i^(4k+1)+i^(4k+2)+i^(4k+3) = ..........

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  2. (1-i)-(-1+i6)=.........

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  3. Multiplicative inverse of complex number z = 2 - 3i is ............

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  4. Express (5-3i)^(3) in the form a+ib.

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  5. z = (1+i)/(1-i) then z^4 = .......... .

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  6. If |z1|=|z2|=|z3|=|(1)/z1+1/z2+1/z3|=1 then |z1+z2+z3| = ...... .

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  7. If one complex number is in third quadrent then its conjugate complex ...

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  8. Complex number with magnitude 2 and argument (2pi)/3 is = .......... .

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  9. If z = (x,-y) then point (x,y) with respect to real axis is called.

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  10. What is the general form of the points which lie on X-axis?

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  11. If |z| = 2 and arg z = (pi)/4 then z = ........

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  12. (1+i)^(4)+(1-i)^(4) = ........ .

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  13. Find argument of the complex numbers z = sqrt3 + i

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  14. If (2+5i) z = (3 - 7 i) then z = ......... .

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  15. If ((1+i)/(1-i))^(100)=x +iy then (x,y) = .......

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  16. Conjugate of the complex number is 1/(1-i) then complex number is .......

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  17. arg (-1) = .........

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  18. In Argand figure complex number (1+2i)/(1-i) lies in ......... quadren...

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  19. If z = x + iy and x +iy= (a+ib)/(a-ib) then x^2+y^2=1.

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  20. ......... is the minimum value of n such that (1+i)^(2n) = (1 - i)^(2n...

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