Question

(x + iy)/(x-iy) का कोणांक है, जबकि |x|/|y| >1​

Answer 1

One looks for the complex numbers z=x+iy, z≠0, such that z=z¯2.

In particular, |z|=1. Plugging z=eit in z=z¯2 yields e3it=1 hence t is a multiple of 23π.

The arguments t=0, t=23π and t=43π yield z=1 and z=−12±i3√2 respectively, thus the solutions are (x,y)=(1,0) and (x,y)=(−12,±3√2).

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