if z= r ( cos tita + i.sin tita ) then the value of z/z + z/z is equal to​

if z= r ( cos tita + i.sin tita ) then the value of z/z + z/z is equal to​

1 thought on “if z= r ( cos tita + i.sin tita ) then the value of z/z + z/z is equal to​”

  1. Answer:

    Given : z = r( cosθ + i sin θ )

    To Find : \dfrac{z}{\overline{z}} +\dfrac{\overline{z}}{z}

    z

    z

    +

    z

    z

    Solution:

    z = r( cosθ + i sin θ )

    \overline{z}

    z

    = r( cosθ – i sin θ )

    \dfrac{z}{\overline{z}} +\dfrac{\overline{z}}{z}

    z

    z

    +

    z

    z

    = r( cosθ + i sin θ ) /r ( cosθ – i sin θ ) + r( cosθ – i sin θ ) /r( cosθ + i sin θ )

    = ( cosθ + i sin θ ) / ( cosθ – i sin θ ) + ( cosθ – i sin θ ) / ( cosθ + i sin θ )

    = ( ( cosθ + i sin θ )² + ( cosθ – i sin θ )²) /(cos²θ – i² sin² θ)

    = ( 2( cos²θ + i² sin² θ )) /(cos²θ – i² sin² θ)

    i² = – 1

    = ( 2( cos²θ – sin² θ )) /(cos²θ + sin² θ)

    cos²θ + sin² θ = 1

    cos²θ – sin² θ = cos2θ

    = 2 cos2θ

    \dfrac{z}{\overline{z}} +\dfrac{\overline{z}}{z}

    z

    z

    +

    z

    z

    = 2 cos2θ

    Step-by-step explanation:

    i think this will help u

    MARK ME AS A BRAINIEST

Leave a Comment