What is expand ((x-i)^2)/((x^2+1)^2) ?

The solution to expand ((x-i)^2)/((x^2+1)^2) is (-1+x^2)/(1+x^4+2x^2)-i(2x)/(1+x^4+2x^2)

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expand ((x-i)^2)/((x^2+1)^2)

expand

\frac{( x - i ) ^{2}}{( x ^{2} + 1 ) ^{2}}

\frac{- 1 + x ^{2}}{1 + x ^{4} + 2 x ^{2}} - i \frac{2 x}{1 + x ^{4} + 2 x ^{2}}

Solution steps

\frac{( x - i ) ^{2}}{( x ^{2} + 1 ) ^{2}}

(x^{2} + 1)^{2} = x^{4} + 2 x^{2} + 1

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

(x - i)^{2} = x^{2} - 2 i x - 1

= \frac{x ^{2} - 2 i x - 1}{x ^{4} + 2 x ^{2} + 1}

Rewrite

\frac{x ^{2} - 2 i x - 1}{x ^{4} + 2 x ^{2} + 1}

in standard complex form:

\frac{x ^{2} - 1}{x ^{4} + 2 x ^{2} + 1} - \frac{2 x}{x ^{4} + 2 x ^{2} + 1} i

= \frac{x ^{2} - 1}{x ^{4} + 2 x ^{2} + 1} - \frac{2 x}{x ^{4} + 2 x ^{2} + 1} i

(a \cdot x + b \cdot x^{\frac{1}{2}} + c)^{2}

(sin (x) + 1) (sin (x) - 1) (4 sin (x) + 1)

- 6 (e^{x} - e^{2 x})

x^{\frac{4}{5}} \times (x - 4)^{2}

\frac{e ^{- t} t ^{2} ( 14 + 2 t )}{9} + 15 - 10 t

What is expand ((x-i)^2)/((x^2+1)^2) ?
The solution to expand ((x-i)^2)/((x^2+1)^2) is (-1+x^2)/(1+x^4+2x^2)-i(2x)/(1+x^4+2x^2)