What is 1/(x+iy)+1/(x-iy)<-1 ?

The solution to 1/(x+iy)+1/(x-iy)<-1 is Ellipse with (h,k)=(-1,0),a=1,b=1

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1/(x+iy)+1/(x-iy)<-1

\frac{1}{x + i y} + \frac{1}{x - i y} < - 1

(h, k) = (- 1, 0), a = 1, b = 1

Solution steps

\frac{1}{x + i y} + \frac{1}{x - i y} < - 1

Rewrite

\frac{1}{x + i y} + \frac{1}{x - i y} < - 1

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{1 ^{2}} + \frac{( y - 0 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = 1, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), b = 1, a = 1

\frac{1}{2} (x - y)^{2} + \frac{1}{2} (x - y) (x + y) + \frac{1}{2} (x + y)^{2} = 4

6 x^{2} + 9 y^{2} - 24 x - 54 y + 51 = 0

\frac{( x + 3 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

\frac{( x - 2 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{25} = 1

\frac{( x - 2 ) ^{2}}{2} + \frac{( y - 4 ) ^{2}}{9} = 1

What is 1/(x+iy)+1/(x-iy)<-1 ?
The solution to 1/(x+iy)+1/(x-iy)<-1 is Ellipse with (h,k)=(-1,0),a=1,b=1