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

1 + 3.322 lo g_{10} (60)

(- 4 x - 3 y) + (- 8 x - y)

a^{7} - a^{20} + a^{14}

15 n^{3} + 12 n

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