What is ((1-i)^{10})/((1+i)^3) ?

The solution to ((1-i)^{10})/((1+i)^3) is -8+8i

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simplify ((1-i)^{10})/((1+i)^3)

simplify

\frac{( 1 - i ) ^{10}}{( 1 + i ) ^{3}}

- 8 + 8 i

Solution steps

\frac{( 1 - i ) ^{10}}{( 1 + i ) ^{3}}

Expand

(1 + i)^{3} : 2 i - 2

= \frac{( 1 - i ) ^{10}}{2 i - 2}

Factor

2 i - 2 : 2 (i - 1)

= \frac{( 1 - i ) ^{10}}{2 ( i - 1 )}

(1 - i)^{10} = (i - 1)^{10}

= \frac{( i - 1 ) ^{10}}{2 ( i - 1 )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(i - 1)^{10} = (i - 1) (i - 1)^{9}

= \frac{( i - 1 ) ( i - 1 ) ^{9}}{2 ( i - 1 )}

Cancel the common factor:

i - 1

= \frac{( i - 1 ) ^{9}}{2}

Simplify

\frac{( i - 1 ) ^{9}}{2} : 8 i - 8

= 8 i - 8

Rewrite in standard complex form:

- 8 + 8 i

= - 8 + 8 i

4 (- 2)

6 - \frac{x}{4} = \frac{x}{8}

\frac{- x}{4} + \frac{x}{3} = - 5

12500

4 x^{2} + 12 x + 11 = 0

What is ((1-i)^{10})/((1+i)^3) ?
The solution to ((1-i)^{10})/((1+i)^3) is -8+8i