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Popular >

simplify (5+i)/(5-i)

Solution

simplify

\frac{5 + i}{5 - i}

Solution

\frac{12}{13} + \frac{5}{13} i

Solution steps

\frac{5 + i}{5 - i}

Multiply by the conjugate

\frac{5 + i}{5 + i}

= \frac{( 5 + i ) ( 5 + i )}{( 5 - i ) ( 5 + i )}

Simplify

\frac{( 5 + i ) ( 5 + i )}{( 5 - i ) ( 5 + i )} : \frac{10 i + 24}{26}

= \frac{10 i + 24}{26}

Rewrite in standard complex form:

\frac{12}{13} + \frac{5}{13} i

= \frac{12}{13} + \frac{5}{13} i

Popular Examples

10 - \frac{x}{6} = 10

simplify 1/((1+e^{-0.7))}simplify

\frac{1}{( 1 + e ^{- 0.7} )}

5k+2<= 18\lor 4k-4>20

5 k + 2 \leq 18 or 4 k - 4 > 20

simplify \sqrt[3]{18}*\sqrt[3]{9}simplify

(x-2)/(2*x-5)=<0

\frac{x - 2}{2 \cdot x - 5} =< 0

Frequently Asked Questions (FAQ)

What is (5+i)/(5-i) ?
The solution to (5+i)/(5-i) is 12/13+5/13 i