# 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​”

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:

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