The complex numbers sinx+icos2x and cosx-isin2x are conjugate to each other for Options: A . &nbspx = nπ B . &nbspx = (n+12)π C . &nbspx=0 D . &nbspNo value of x

Answer: Option D : D sinx+icos2x and cosx-isin2xare conjugate to each other if sinx=cosxand cos2x=sin2x Or tan x = 1 ⇒ x = π 4 , 5 π 4 , 9 π 4 , .......... ...............(i) And tan 2x = 1⇒ 2x = π 4 , 5 π 4 , 9 π 4 , .......... or x = π 8 , 5 π 8 , 9 π 8 , .......... ...............(ii) There exists no value of xcommon in (i) and (ii). Therefore there is no value of xfor which the given complex numbers are conjugate.

The complex numbers sinx+icos2x and cosx-isin2x are conjugate to each

Question

The complex numbers sinx+icos2x and cosx-isin2x are conjugate to each other for

Options:

A . x = nπ

B . x = (n+12)π

C . x=0

D . No value of x

Answer: Option D
:
D
sinx+icos2x and cosx-isin2xare conjugate to each other if sinx=cosxand cos2x=sin2x
Or tan x = 1 ⇒ x =

\frac{π}{4}

\frac{5 π}{4}

\frac{9 π}{4}

, .......... ...............(i)
And tan 2x = 1⇒ 2x =

\frac{π}{4}

\frac{5 π}{4}

\frac{9 π}{4}

, ..........
or x =

\frac{π}{8}

\frac{5 π}{8}

\frac{9 π}{8}

, .......... ...............(ii)
There exists no value of xcommon in (i) and (ii). Therefore there is no value of xfor which the given complex numbers are conjugate.

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