By simplifying $$i^{18}-3 i^7+i^2\left(1+i^4\right)(i)^{22}$$, we get

The values of $$x$$ for which $$\sin x+i \cos 2 x$$ and $$\cos x-i \sin 2 x$$ are conjugate to each other are

The locus of a point $$z$$ satisfying $$|z|^2=\operatorname{Re}(z)$$ is a circle with centre

Multiplicative inverse of the complex number $$(\sin \theta, \cos \theta)$$ is