What is 1/(1+\frac{1){1-1/(1+i)}} ?

The solution to 1/(1+\frac{1){1-1/(1+i)}} is 2/5+1/5 i

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simplify 1/(1+\frac{1){1-1/(1+i)}}

simplify

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

\frac{2}{5} + \frac{1}{5} i

Solution steps

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

Simplify

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

= \frac{1}{2 - i}

Multiply by the conjugate

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

= \frac{1 \cdot ( 2 + i )}{( 2 - i ) ( 2 + i )}

Simplify

\frac{1 \cdot ( 2 + i )}{( 2 - i ) ( 2 + i )} : \frac{2 + i}{5}

= \frac{2 + i}{5}

Rewrite in standard complex form:

\frac{2}{5} + \frac{1}{5} i

= \frac{2}{5} + \frac{1}{5} i

\frac{6}{4 - i}

\frac{\frac{15}{17}}{\frac{8}{17}}

12 b^{2} - 6 b

ln (2) - ln (3)

\frac{1}{14} + 1

What is 1/(1+\frac{1){1-1/(1+i)}} ?
The solution to 1/(1+\frac{1){1-1/(1+i)}} is 2/5+1/5 i