Question 3

What is the value of $$(2-2z+z^{2})(2+2z-z^{2})$$, when $$z+\frac{2}{z}=2$$ ?

Solution

Given : $$z+\frac{2}{z}=2$$

=> $$\frac{z^2+2}{z}=2$$

=> $$z^2=2z-2$$ -----------(i)

To find : $$(2-2z+z^{2})(2+2z-z^{2})$$

Substituting value from equation (i), we get :

= $$[2-2z+(2z-2)][2+2z-(2z-2)]$$

= $$(0)\times(0)=0$$

=> Ans - (A)

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