Question

find the real value of theta such that 1+i cos theta /1-2i cos theta is a real number
​

Answer 1

Step-by-step explanation:

Let z=

1−2icosθ

1+icosθ

=

(1−2icosθ)(1+2icosθ)

(1+icosθ)(1+2icosθ)

=

1+4cos

2

θ

1−2cos

2

θ+i3cosθ

=

1+4cos

2

θ

1−2cos

2

θ

+i(

1+4cos

2

θ

3cosθ

)

If the above complex number is purely real, then

Im(z)=0

3cosθ=0

θ=

2

(2n±1)π

, where nϵN

Answer 2

Answer:

Hope this helps you.

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