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Popular >

simplify (i/(1+i))^5

Solution

simplify

(\frac{i}{1 + i})^{5}

Solution

\frac{i ( - 1 + i )}{8}

Solution steps

(\frac{i}{1 + i})^{5}

Simplify

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

= (\frac{i ( 1 - i )}{2})^{5}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( i ( 1 - i ) ) ^{5}}{2 ^{5}}

Simplify

(i (1 - i))^{5} : i (4 i - 4)

= \frac{i ( 4 i - 4 )}{2 ^{5}}

2^{5} = 32

= \frac{i ( 4 i - 4 )}{32}

Simplify

\frac{i ( 4 i - 4 )}{32} : \frac{i ( i - 1 )}{8}

= \frac{i ( i - 1 )}{8}

Rewrite in standard complex form:

\frac{i ( - 1 + i )}{8}

= \frac{i ( - 1 + i )}{8}

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Frequently Asked Questions (FAQ)

What is (i/(1+i))^5 ?
The solution to (i/(1+i))^5 is (i(-1+i))/8