What is i/(i^2+2i-1) ?

The solution to i/(i^2+2i-1) is 1/4-1/4 i

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simplify i/(i^2+2i-1)

simplify

\frac{i}{i ^{2} + 2 i - 1}

\frac{1}{4} - \frac{1}{4} i

Solution steps

\frac{i}{i ^{2} + 2 i - 1}

Simplify

i^{2} + 2 i - 1 : 2 i - 2

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

Rewrite

2 i - 2

in standard complex form:

- 2 + 2 i

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

Multiply by the conjugate

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

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

Simplify

\frac{i ( - 2 - 2 i )}{( - 2 + 2 i ) ( - 2 - 2 i )} : \frac{- 2 i + 2}{8}

= \frac{- 2 i + 2}{8}

Rewrite in standard complex form:

\frac{1}{4} - \frac{1}{4} i

= \frac{1}{4} - \frac{1}{4} i

(\frac{1}{32})^{- \frac{1}{5}}

\frac{1 + 6 i}{5 i}

(5)^{2} + (12)^{2}

\frac{( 6 y ) ^{5}}{( 3 y ) ^{4}}

(\frac{6}{5})^{3}