let   a+ib=tan^-1(x+iy)

      a-ib=tan^-(x-iy)

-----------------------------(add)

2a  = tan^-(x+iy)+tan ^-1(x-iy)

2a = tan^-1( 2x/1-(x²+y²))

tan2a = 2x/1-(x²+y² )  there for x²+y²+2xcota =1

Complex number is an angle in argand plane

Argand plane is just like coordintae plane, but difference is that y-axis is imaginary and x-axis is real.

Eg:- for complex number z = a + ib, the point in argand plane will be (a,b)

for z = c + id it will be (c,d)

for z = e + ig it will be (e,g)

Now angle on that plane is tan = b/a for z = a + ib, tan = d/c for z = c + id. [Also we consider sign of a,b or c,d]