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Popular >

simplify i/(i+1)

Solution

simplify

\frac{i}{i + 1}

Solution

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

Solution steps

\frac{i}{i + 1}

Rewrite

i + 1

in standard complex form:

1 + i

= \frac{i}{1 + i}

Multiply by the conjugate

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

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

Simplify

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

= \frac{i + 1}{2}

Rewrite in standard complex form:

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

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

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Frequently Asked Questions (FAQ)

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