What is ((1+i)^{19})/((1-i)^{17)} ?

The solution to ((1+i)^{19})/((1-i)^{17)} is -2

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simplify ((1+i)^{19})/((1-i)^{17)}

simplify

\frac{( 1 + i ) ^{19}}{( 1 - i ) ^{17}}

- 2

Solution steps

\frac{( 1 + i ) ^{19}}{( 1 - i ) ^{17}}

Expand

(1 + i)^{19} : 512 i - 512

= \frac{512 i - 512}{( 1 - i ) ^{17}}

Expand

(1 - i)^{17} : - 256 i + 256

= \frac{512 i - 512}{- 256 i + 256}

Factor

512 i - 512 : 512 (i - 1)

= \frac{512 ( i - 1 )}{- 256 i + 256}

Factor

- 256 i + 256 : 256 (- i + 1)

= \frac{512 ( i - 1 )}{256 ( - i + 1 )}

Factor the number:

512 = 256 \cdot 2

= \frac{256 \cdot 2 ( i - 1 )}{256 ( - i + 1 )}

Cancel the common factor:

256

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

Factor

- i + 1 : - (i - 1)

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

Cancel the common factor:

i - 1

= \frac{2}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - 2

(3 x - y = 4,) (x + y = 3)

\frac{( x + 2 ) ^{2}}{2}

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(n^{5} + 100) (32 lo g_{10} (n) - 6)

(cot (θ) + csc (θ)) (tan (θ) - sin (θ))

What is ((1+i)^{19})/((1-i)^{17)} ?
The solution to ((1+i)^{19})/((1-i)^{17)} is -2