What is (1+b+ia)/(1+b-ia)=b+ia ?

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

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(1+b+ia)/(1+b-ia)=b+ia

\frac{1 + b + ia}{1 + b - ia} = b + ia

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

Solution steps

\frac{1 + b + ia}{1 + b - ia} = b + ia

Rewrite

\frac{1 + b + ia}{1 + b - ia} - b - ia = 0

in the form of the standard ellipse equation

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

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