What is simplify-(2(1-i)^7)/((1+i)^7) ?

The solution to simplify-(2(1-i)^7)/((1+i)^7) is -2i

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simplify-(2(1-i)^7)/((1+i)^7)

simplify

- \frac{2 ( 1 - i ) ^{7}}{( 1 + i ) ^{7}}

- 2 i

Solution steps

- \frac{2 ( 1 - i ) ^{7}}{( 1 + i ) ^{7}}

Expand

(1 + i)^{7} : - 8 i + 8

= - \frac{2 ( 1 - i ) ^{7}}{- 8 i + 8}

Factor

- 8 i + 8 : 8 (- i + 1)

= - \frac{2 ( 1 - i ) ^{7}}{8 ( - i + 1 )}

Factor the number:

8 = 2 \cdot 4

= - \frac{2 ( 1 - i ) ^{7}}{2 \cdot 4 ( - i + 1 )}

Cancel the common factor:

2

= - \frac{( 1 - i ) ^{7}}{4 ( - i + 1 )}

Apply the commutative law:

1 - i = - i + 1

= - \frac{( - i + 1 ) ^{7}}{4 ( - i + 1 )}

Apply exponent rule:

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

(- i + 1)^{7} = (- i + 1) (- i + 1)^{6}

= - \frac{( - i + 1 ) ( - i + 1 ) ^{6}}{4 ( - i + 1 )}

Cancel the common factor:

- i + 1

= - \frac{( - i + 1 ) ^{6}}{4}

Simplify

- \frac{( - i + 1 ) ^{6}}{4} : - 2 i

= - 2 i

(x - 3) (x - 2 - \frac{4}{x - 3})

\frac{W L ( 2 X - L ) ^{2}}{8}

A (- 2, 1) B (3, 4) C (5, - 2)

\frac{s ^{4} + 2 s ^{3} - 2 s ^{2} - 2 s + 2}{s ^{2} ( s - 1 )}

\frac{a - b \cdot i}{1 + ( a + b \cdot i ) ^{2}}

What is simplify-(2(1-i)^7)/((1+i)^7) ?
The solution to simplify-(2(1-i)^7)/((1+i)^7) is -2i