Home
Class 12
MATHS
If (x-alpha)/(z+alpha)(alpha in R) is a ...

If `(x-alpha)/(z+alpha)(alpha in R)` is a purely imaginery number and `|z|=2`, then a value of `alpha` is

A

`(1)/(2)`

B

1

C

`sqrt(2)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
`(z-alpha)/(z+alpha)+(overline(z)-alpha)/(overline(z)+alpha)=0`
`(zoverline(z)+zalpha-overline(z)alpha-alpha^(2)+zoverline(z)-zalpha+overline(z)-alpha^2)/((z+alpha)(z+alpha))=0`
`2|z|^2-2alpha^2=0`
`alpha^2=4`.
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST 8 (2020)

    VMC MODULES ENGLISH|Exercise MATHEMATICS ( SECTION 2 )|5 Videos

  • JEE MAIN REVISION TEST 5 (2020)

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • JEE MAIN REVISION TEST- 16

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

(z-alpha)/(z+alpha) is purely imaginary and |z|=82 then |alpha| is:

Let (z-alpha)/(z+alpha) is purely imaginary and |z|=2, alpha in RR then alpha is equal to (A) 2 (B) 1 (C) sqrt2 (D) sqrt3

Let (z-alpha)/(z+alpha) is purely imaginary and |z|=2, alphaepsilonR then alpha is equal to (A) 2 (B) 1 (C) sqrt2 (D) sqrt3

Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation. Find the values of alpha for which Both the roots are opposite in sign

Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation. Find the values of alpha for which Both the roots are equal in magnitude but opposite in sign

If z = ((1+i)^(2))/(alpha-i) , alpha in R has magnitude sqrt((2)/(5)) then the value of alpha is (i) 3 only (ii) -3 only (iii) 3 or -3 (iv) none of these

Let alpha be a real number such that 0 <= alpha <= pi. If f(x)=cosx+cos(x+alpha)+cos(x+2alpha) takes some constant number c for any x in R, then the value of [c + alpha] is equal to (Note : [y] denotes greatest integer less than or equal to y.)

if (tanalpha-i(sin ""(alpha)/(2)+cos ""(alpha)/(2)))/(1+2 i sin ""(alpha)/(2)) is purely imaginary then alpha is given by -

if A=[{:(alpha,2),(2, alpha):}] and |A|^(3)=125 then the value of alpha is

Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i)]^2+[(a-b i)//(a+b i)]^2 , where a ,b , in R and beta=(z-1)//(z+1), w here |z|=1, then find the correct statement: both alphaa n dbeta are purely real both alphaa n dbeta are purely imaginary alpha is purely real and beta is purely imaginary beta is purely real and alpha is purely imaginary