What is expand (e^2i)/((R+i)^2) ?

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

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expand (e^2i)/((R+i)^2)

expand

\frac{e ^{2} i}{( R + i ) ^{2}}

\frac{2 e ^{2} R}{1 + R ^{4} + 2 R ^{2}} + i \frac{- e ^{2} + e ^{2} R ^{2}}{1 + R ^{4} + 2 R ^{2}}

Solution steps

\frac{e ^{2} i}{( R + i ) ^{2}}

(R + i)^{2} = R^{2} + 2 i R - 1

= \frac{e ^{2} i}{R ^{2} + 2 i R - 1}

Rationalize

\frac{e ^{2} i}{R ^{2} + 2 i R - 1} : \frac{2 e ^{2} R + e ^{2} i ( R ^{2} - 1 )}{R ^{4} + 2 R ^{2} + 1}

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

Rewrite

\frac{2 e ^{2} R + e ^{2} i ( R ^{2} - 1 )}{R ^{4} + 2 R ^{2} + 1}

in standard complex form:

\frac{2 e ^{2} R}{R ^{4} + 2 R ^{2} + 1} + \frac{e ^{2} R ^{2} - e ^{2}}{R ^{4} + 2 R ^{2} + 1} i

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

\frac{4 x ^{2} ( 30 - 2 x )}{9}

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

\frac{( 2 x + 3 )}{( x - 5 ) ( x + 4 )}

z [(n - 1) a^{n - 1}]

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

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