113rd one should not be difficult either....
It's a std arithmetico-geometric series......
Q.1) If A and B represent complex number z1 and z2 in the argand plane,then how r the slope and complex slope of AB is defined ?
To find the line perpendicular to a line: az' + a'z + b = 0, is the slope or the complex slope considered ?
(here, a' and z' represent the conjugates of a and z respectively)
Q.2) If arg z = ∂ , where ( -∩ < ∂ ≤ ∩) , then locus of z is a half-line. HOW ?
( ∩ represents pi )
Q.3) If ∂ be the non-real nth root of unity,then
1 + 3∂ + 5∂2 +.......... (2n-1) ∂n-1 = ?
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11 Answers
106Q2. Arg(z) of any complex number lies between -∩ and ∩ .. Let a complex number have argument θ which is [0,∩/2] then the complex number is in 1st quadrant only.
So it is a half line making angle θ with x-axis and passing through the origin
11)the complex slope of z1 and z2 is defined as z1 - z2-z1 -z2
2) tan π =xy=0 ; y =constant as x=0
11106Q4. If l z-3+2i l ≤ 4, where i=√-1 then the difference of the greatest and the least values of lzl is ?
Q5. If z1 and z2 are any two complex numbers, then
l z1 + √z12+z22 l + l z1 - √z12-z22 l is equal to
(a) l z1 l (b) lz2l (c) l z1 +z2 l (d) none
Q6. The set of points in an argand diagram which satisfy both lzl≤4 and arg(z)=∩/3 is
(a) a circle and a line
(b) a radius of a circle
(c) a sector of a circle
(d) an infinite part line
(i thot that the answer wud be (b) but it is given (c))
3Q4) represents a disc having its center at (3,-2) so u can find the greatest and the minimum value of mod(z)
q5)none
106sankara can u please post the solution im not able to follow (Q4.)
explain Q5 also
1Q4. If l z-3+2i l ≤ 4, where i=√-1 then the difference of the greatest and the least values of lzl is ?
it represents d interior of d circle wid centre at (3,-2)
so nw d greatest n least distnce will b eithr ends of diametr
draw d circle then a line thru origin ......n then ..... least means d oen on nearer end n greatst means furthr end
3mrunal the locus is not a circle it will be a circle if mod(z-3+2i) is =4
since all the pts interior to the circle satisfies the equation therefore it represents a disc centerd at (3,-2)
106Q7. If αo,α1,α2,....,αn-1 be the n, nth roots of unity, then the value of
\sum_{i=0}^{n-1}{\frac{\alpha _{i}}{(3-\alpha _{i}}} is equal to
(a) n/(3n-1) (b) (n-1)/(3n-1) (c) (n+1)/(3n-1) (d) (n+2)/(3n-1)
24for Q7 read this thread...Nishant sir helped me there
http://targetiit.com/iit-jee-forum/posts/help-karo-3064.html
39for question 7 substitute n=2 and get the answer.
really sorry asish have a departmental orientation right now. will solve it surely i login next time(i have noted down it in my note book)
