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Popular >

simplify (x+8i)/(x-8i)

Solution

simplify

\frac{x + 8 i}{x - 8 i}

Solution

\frac{x ^{2} - 64}{x ^{2} + 64} + \frac{16 x}{x ^{2} + 64} i

Solution steps

\frac{x + 8 i}{x - 8 i}

Multiply by the conjugate

\frac{x + 8 i}{x + 8 i}

= \frac{( x + 8 i ) ( x + 8 i )}{( x - 8 i ) ( x + 8 i )}

Simplify

\frac{( x + 8 i ) ( x + 8 i )}{( x - 8 i ) ( x + 8 i )} : \frac{x ^{2} + 16 x i - 64}{x ^{2} + 64}

= \frac{x ^{2} + 16 x i - 64}{x ^{2} + 64}

Rewrite in standard complex form:

\frac{x ^{2} - 64}{x ^{2} + 64} + \frac{16 x}{x ^{2} + 64} i

= \frac{x ^{2} - 64}{x ^{2} + 64} + \frac{16 x}{x ^{2} + 64} i

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Frequently Asked Questions (FAQ)

What is (x+8i)/(x-8i) ?
The solution to (x+8i)/(x-8i) is (x^2-64)/(x^2+64)+(16x)/(x^2+64)i