What is (x+iy)/(x-iy) ?

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

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simplify (x+iy)/(x-iy)

simplify

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

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

Solution steps

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

Rewrite

x + i y

in standard complex form:

x + y i

Rewrite

x - i y

in standard complex form:

x - y i

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

Multiply by the conjugate

\frac{x + y i}{x + y i}

= \frac{( x + y i ) ( x + y i )}{( x - y i ) ( x + y i )}

Simplify

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

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

Rewrite 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

m^{3} + 3 m^{2} - 4

\frac{1}{4} \times \frac{1}{6}

(x - i y)^{3}

2 \times 13

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