f x+iy=11+cosθ+isinθ𝑥+𝑖𝑦=11+cos𝜃+𝑖sin𝜃, then 4x2−1=

The given equation is x + iy = 11 + cosθ + isinθ.

First, we can equate the real and imaginary parts on both sides of the equation.

This gives us:

x = 11 + cosθ (equation 1)

and

y = sinθ (equation 2)

We are asked to find the value of 4x² - 1.

Substituting equation 1 into this, we get:

4x² - 1 = 4(11 + cosθ)² - 1

= 4(121 + 22cosθ + cos²θ) - 1

= 484 + 88cosθ + 4cos²θ - 1

= 483 + 88cosθ + 4cos²θ

This is the expression for 4x² - 1 in terms of θ.

Please note that without a specific value for θ, we cannot simplify this further.