What is expand ((x-iy)^2)/(x^2+y^2) ?

The solution to expand ((x-iy)^2)/(x^2+y^2) is (x^2-y^2)/(x^2+y^2)-i(2xy)/(x^2+y^2)

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expand ((x-iy)^2)/(x^2+y^2)

expand

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

\frac{x ^{2} - y ^{2}}{x ^{2} + y ^{2}} - i \frac{2 x y}{x ^{2} + y ^{2}}

Solution steps

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

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

= \frac{x ^{2} - 2 i x y - y ^{2}}{x ^{2} + y ^{2}}

Rewrite

\frac{x ^{2} - 2 i x y - y ^{2}}{x ^{2} + y ^{2}}

in standard complex form:

\frac{x ^{2} - y ^{2}}{x ^{2} + y ^{2}} - \frac{2 x y}{x ^{2} + y ^{2}} i

= \frac{x ^{2} - y ^{2}}{x ^{2} + y ^{2}} - \frac{2 x y}{x ^{2} + y ^{2}} i

e^{2 (x + y i)}

\frac{x ( x + 1 ) ( x + 2 )}{6}

\frac{π ( e ^{3} - 1 )}{3 e ^{3}}

(4 a^{2} - 3 b + 2 c d - 5 e)^{2}

(2 x^{3} - 4 x^{2} + 1)^{5}

What is expand ((x-iy)^2)/(x^2+y^2) ?
The solution to expand ((x-iy)^2)/(x^2+y^2) is (x^2-y^2)/(x^2+y^2)-i(2xy)/(x^2+y^2)