What is (x+iy)^2+(x-iy)^2=2 ?

The solution to (x+iy)^2+(x-iy)^2=2 is Hyperbola with (h,k)=(0,0),a=1,b=1

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(x+iy)^2+(x-iy)^2=2

(x + i y)^{2} + (x - i y)^{2} = 2

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

Solution steps

(x + i y)^{2} + (x - i y)^{2} = 2

Rewrite

(x + i y)^{2} + (x - i y)^{2} = 2

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

y^{2} = x^{2} + 25

y^{2} = x^{2} + 49

x^{2} - 4 x - 4 y^{2} - 8 y - 16 = 0

25 x^{2} - 16 y^{2} + 300 x + 64 y + 436 = 0

What is (x+iy)^2+(x-iy)^2=2 ?
The solution to (x+iy)^2+(x-iy)^2=2 is Hyperbola with (h,k)=(0,0),a=1,b=1