The complex numbers $\sin x+i \cos 2 x$ and $\cos x$ - $\mathrm{i} \sin 2 x,(\mathrm{i}=\sqrt{-1})$ are conjugate to each other for,

The value of $\frac{(\cos \theta+i \sin \theta)^4}{(\sin \theta+i \cos \theta)^5}=$ where $\mathrm{i}=\sqrt{-1}$

The equation $|z+1-i|=|z-1+i|$ represents a (where z is a complex number)

If $\frac{z-1}{2 z+1}$ is an imaginary number and if it represents a circle then its radius is