What is 4/(x+yi)=x-yi ?

The solution to 4/(x+yi)=x-yi is Ellipse with (h,k)=(0,0),a=2,b=2

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4/(x+yi)=x-yi

\frac{4}{x + y i} = x - y i

(h, k) = (0, 0), a = 2, b = 2

Solution steps

\frac{4}{x + y i} = x - y i

Rewrite

\frac{4}{x + y i} - x + y i = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 2, a = 2

4 (x + 3)^{2} + y^{2} = 16

2 (1 + 2 y) (y - 2) = - (2 x - 3) (x - 7)

\frac{( x + 1 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{36} = 1

\frac{( x + 4 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{16} = 1

(x^{2} + 10 x) + (4 y^{2} + 9 y) = 7

What is 4/(x+yi)=x-yi ?
The solution to 4/(x+yi)=x-yi is Ellipse with (h,k)=(0,0),a=2,b=2