What is (sqrt(2)-i)/(sqrt(2)+2i) ?

The solution to (sqrt(2)-i)/(sqrt(2)+2i) is -1/(sqrt(2))i

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simplify (sqrt(2)-i)/(sqrt(2)+2i)

simplify

\frac{2 - i}{2 + 2 i}

- \frac{1}{2} i

Solution steps

\frac{2 - i}{2 + 2 i}

Multiply by the conjugate

\frac{2 - 2 i}{2 - 2 i}

= \frac{( 2 - i ) ( 2 - 2 i )}{( 2 + 2 i ) ( 2 - 2 i )}

Simplify

\frac{( 2 - i ) ( 2 - 2 i )}{( 2 + 2 i ) ( 2 - 2 i )} : \frac{- 3 2 i}{6}

= \frac{- 3 2 i}{6}

Cancel

\frac{- 3 2 i}{6} : - \frac{i}{2}

= - \frac{i}{2}

Rewrite in standard complex form:

- \frac{1}{2} i

= - \frac{1}{2} i

x + 2 < \frac{x}{x + 2}

8 a^{2} + 16 b^{2}

276 + 7150

- 5 \leq 2 a - 1 < 9

7 x + 3 = x - 3

What is (sqrt(2)-i)/(sqrt(2)+2i) ?
The solution to (sqrt(2)-i)/(sqrt(2)+2i) is -1/(sqrt(2))i