What is ((1-sqrt(3)i)^5)/((1+i)^4) ?

The solution to ((1-sqrt(3)i)^5)/((1+i)^4) is -4-4sqrt(3)i

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simplify ((1-sqrt(3)i)^5)/((1+i)^4)

simplify

\frac{( 1 - 3 i ) ^{5}}{( 1 + i ) ^{4}}

- 4 - 43 i

Solution steps

\frac{( 1 - 3 i ) ^{5}}{( 1 + i ) ^{4}}

Expand

(1 - 3 i)^{5} : 163 i + 16

= \frac{16 3 i + 16}{( 1 + i ) ^{4}}

Expand

(1 + i)^{4} : - 4

= \frac{16 3 i + 16}{- 4}

Factor out common term

16 : 16 (3 i + 1)

= \frac{16 ( 3 i + 1 )}{- 4}

Divide the numbers:

\frac{16}{- 4} = - 4

= - 4 (3 i + 1)

Expand

- 4 (3 i + 1) : - 43 i - 4

= - 43 i - 4

Rewrite in standard complex form:

- 4 - 43 i

= - 4 - 43 i

\frac{2 7 - 3}{7 + 2}

\frac{120}{7}

5.3 x - 8.14 + 3.6 x + 9.8

(3 m - 4)^{3} (3 m^{5})

\frac{cos ( x )}{1 + sin ( x )} - \frac{cos ( x )}{1 - sin ( x )}

What is ((1-sqrt(3)i)^5)/((1+i)^4) ?
The solution to ((1-sqrt(3)i)^5)/((1+i)^4) is -4-4sqrt(3)i