If `(3)/(2+costheta+isintheta)=a+ib` where `i=sqrt(-1)anda^(2)+b^(2)=lamdaa-3,` the value of `lamda` is

A

3

B

4

C

5

D

6

Verified by Experts

Similar Questions

Explore conceptually related problems

If z^(3)+(3+2i)z+(-1+ia)=0, " where " i=sqrt(-1) , has one real root, the value of a lies in the interval (a in R)

if cos (1-i) = a+ib, where a , b in R and i = sqrt(-1) , then

Let z=costheta+isintheta . Then the value of sum_(m=1)^15 Im(z^(2m-1)) at theta=2^@ is:

If z is any complex number satisfying abs(z-3-2i) le 2 , where i=sqrt(-1) , then the minimum value of abs(2z-6+5i) , is

If alpha and beta are the complex roots of the equation (1+i)x^(2)+(1-i)x-2i=0 where i=sqrt(-1) , the value of |alpha-beta|^(2) is

If the following equations x+y-3 = 0, (1+lamda)x + (2+lamda) y - 8 = 0, x-(1+lamda)y + (2+lamda) = 0 are consistent then the value of lamda is

Statement-1: 3+7i gt 2+4i, where i=sqrt(-1). Statement-2: 3 gt 2 and 7 gt 4

If |z-2-3i|+|z+2-6i|=4 where i=sqrt(-1) then find the locus of P(z)

Let z=9+ai, where i=sqrt(-1) and a be non-zero real. If Im(z^(2))=Im(z^(3)) , sum of the digits of a^(2) is

If z=(sqrt(3)-i)/2 , where i=sqrt(-1) , then (i^(101)+z^(101))^(103) equals to