Home
Class 12
MATHS
If z is a complex number lying in the fo...

If `z` is a complex number lying in the fourth quadrant of Argand plane and `|[(kz)/(k+1)]+2i|>sqrt(2)` for all real value of`k(k!=-1),` then range of `"arg"(z)` is `(pi/8,0)` b. `(pi/6,0)` c.`(pi/4,0)` d. none of these

Text Solution

Verified by Experts

The given inequality is ` |(kz)/(k+1) + 2i|gt sqrt2`
`Rightarrow |z-((-2i)(k+1))/k|gt(sqrt2(k+1))/k`
Which represents the region lying outside the circle centred
`at(0,(-2(k+1))/k) and " radius " (sqrt2(k+1))/k`
let `COP =theta` so that
`sin theta= (CP)/(OC) = ((sqrt2(k+1))/k)/((2(k+1))/k)=1/sqrt2 = sinpi//4`
` theta= pi/4`
Since z lies in the `IV^("th")` quadrant, hence
` arg z "in" ( - pi/4, 0)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|60 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

Similar Questions

Explore conceptually related problems

If z ne 0 be a complex number and "arg"(z)=pi//4 , then

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

A variable complex number z is such that the amplitude of (z-1)/(z+1) is always equal to (pi)/(4) Illustrate the locus of z in the Argand plane

Find the locus of a complex number z= x+ yi satisfying the relation arg (z-a)=(pi)/(4), a in R Illustrate the locus of z in the Argand plane

A variable complex number z is such that the amplitude of (z-1)/(z+1) is always equal to (pi)/(4) . Illustrate the locus of z in the Argand plane

For a complex number Z, if arg Z=(pi)/(4) and |Z+(1)/(Z)|=4 , then the value of ||Z|-(1)/(|Z|)| is equal to

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is (a)[0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

Let Z and w be two complex number such that |zw|=1 and arg(z)−arg(w)=pi//2 then

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

A variable complex number z=x+iy is such that arg (z-1)/(z+1)= pi/2 . Show that x^2+y^2-1=0 .