What is (sqrt(2)(1-i)^5)/8 ?

The solution to (sqrt(2)(1-i)^5)/8 is -1/(sqrt(2))+1/(sqrt(2))i

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simplify (sqrt(2)(1-i)^5)/8

simplify

\frac{2 ( 1 - i ) ^{5}}{8}

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

Solution steps

\frac{2 ( 1 - i ) ^{5}}{8}

Factor the number:

8 = 2 \cdot 4

= \frac{2 ( 1 - i ) ^{5}}{2 \cdot 4}

Apply radical rule:

a = a a

2 = 22

= \frac{2 ( 1 - i ) ^{5}}{2 2 \cdot 4}

Cancel the common factor:

2

= \frac{( 1 - i ) ^{5}}{2 \cdot 4}

Cancel

\frac{( 1 - i ) ^{5}}{2 \cdot 4} : - \frac{1}{2} + \frac{1}{2} i

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

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What is (sqrt(2)(1-i)^5)/8 ?
The solution to (sqrt(2)(1-i)^5)/8 is -1/(sqrt(2))+1/(sqrt(2))i