IIT JEE , AIEEE Forum - Mathematics , Algebra - complex nos

priyesh

Let Z(

,

) = cos

+ eⁱsin

(

,

R, i =

-1 ), then the range of values of modulus of Z(

,2

) as

varies , is

A) [

2 ,

3] B) [1,

2]

C) [ 1/

3 ,

2/

3] D) [ 1/

2 ,

3/

2]

priyesh

someone pls solve

nadeemoidu

D)
$Z(\theta , 2\theta ) = \cos \theta + e^{i2\theta} \sin \theta$

$= \cos \theta + (\cos 2\theta+ i \sin 2\theta ) \sin \theta$

$|Z|^2 = ( \cos \theta + \cos 2 \theta \sin \theta ) ^2 + (\sin 2 \theta \sin\theta)^2$

Now simplify ,
$|Z|^2 = 1 + \frac{\sin 4 \theta }{2}$

priyesh

Thanks nadeemoidu

Ask & Discuss Questions with Community & Experts