What is a-bi= 1/(a+bi) ?

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

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a-bi= 1/(a+bi)

a - bi = \frac{1}{a + bi}

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

Solution steps

a - bi = \frac{1}{a + bi}

Rewrite

a - bi - \frac{1}{a + bi} = 0

in the form of the standard ellipse equation

\frac{( a - 0 ) ^{2}}{1 ^{2}} + \frac{( b - 0 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

x^{2} + 4 y^{2} + 20 x + 44 y + 121 = 0

16 x^{2} + 7 y^{2} = 112

\frac{( x + 1 ) ^{2}}{2} + \frac{y ^{2}}{8} = 1

y^{2} = - 0.25 x^{2} + 1

x, \frac{x ^{2}}{25} + \frac{Y ( x ) ^{2}}{4} = 1

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