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If $x^{2} + y^{2} = 1$ and $x \neq - 1$ then $\frac{1 + y + i x}{1 + y - i x}$ equals

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Correct option is D

TIP Sometimes, it is helpful to write x2+y2=zz¯where z=x+iy or y+ixPut z=y+ix,then 1=x2+y2=zz¯Now,1+y+ix1+y−ix=zz¯+z1+z¯=z(z¯+1)1+z¯=z=y+ix

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If x2+y2=1and x≠−1 then 1+y+ix1+y−ix equals

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If $x^{2} + y^{2} = 1$ and $x \neq - 1$ then $\frac{1 + y + i x}{1 + y - i x}$ equals