What is ((1-i)^7)/((1+i)^9) ?

The solution to ((1-i)^7)/((1+i)^9) is 1/2

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simplify ((1-i)^7)/((1+i)^9)

simplify

\frac{( 1 - i ) ^{7}}{( 1 + i ) ^{9}}

\frac{1}{2}

Decimal Notation

0.5

Solution steps

\frac{( 1 - i ) ^{7}}{( 1 + i ) ^{9}}

Expand

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

= \frac{8 i + 8}{( 1 + i ) ^{9}}

Factor

8 i + 8 : 8 (i + 1)

= \frac{8 ( i + 1 )}{( 1 + i ) ^{9}}

Apply the commutative law:

1 + i = i + 1

= \frac{8 ( i + 1 )}{( i + 1 ) ^{9}}

Apply exponent rule:

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

(i + 1)^{9} = (i + 1) (i + 1)^{8}

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

Cancel the common factor:

i + 1

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

Simplify

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

= \frac{1}{2}

\frac{26}{( x - 1 ) ( x + 1 )}

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(x + 2)^{2}

(x y + y^{2}) d y + (y^{2} + 1) d x