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

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

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simplify ((x+yi))/(x-yi)

simplify

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

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

Solution steps

\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

r^{2} - 3 r - 4 = 0

z^{2} = - (6 z + 7)

x^{4} - 1 \leq - 7 x^{2} + 7

\frac{6 - 2 a}{30}

1 2^{- 1}

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