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

The solution to (-4sqrt(3)+4i)^5 is 16384sqrt(3)+16384i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

(- 43 + 4 i)^{5}

163843 + 16384 i

Solution steps

(- 43 + 4 i)^{5}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = - 43, b = 4 i

= i = 0 \sum 5 (i 5) (- 43)^{(5 - i)} (4 i)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (- 43)^{5} (4 i)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (- 43)^{4} (4 i)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (- 43)^{3} (4 i)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (- 43)^{2} (4 i)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (- 43)^{1} (4 i)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (- 43)^{0} (4 i)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (- 43)^{5} (4 i)^{0} : - 92163

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (- 43)^{4} (4 i)^{1} : 46080 i

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (- 43)^{3} (4 i)^{2} : - 307203 i^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (- 43)^{2} (4 i)^{3} : 30720 i^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (- 43)^{1} (4 i)^{4} : - 51203 i^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (- 43)^{0} (4 i)^{5} : 1024 i^{5}

= - 92163 + 46080 i - 307203 i^{2} + 30720 i^{3} - 51203 i^{4} + 1024 i^{5}

Simplify

- 92163 + 46080 i - 307203 i^{2} + 30720 i^{3} - 51203 i^{4} + 1024 i^{5} : 16384 i + 163843

= 16384 i + 163843

Rewrite in standard complex form:

163843 + 16384 i

= 163843 + 16384 i

2 (x + 2 - x^{2})

\frac{1}{12} (cos (8 t) - 8 sin (8 t))

\frac{2 x}{( x ^{2} + 25 ) ( x - 1 )}

\frac{1}{( 6 + x ) ^{3}}

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

What is (-4sqrt(3)+4i)^5 ?
The solution to (-4sqrt(3)+4i)^5 is 16384sqrt(3)+16384i