What is (8-8sqrt(3)i)^7 ?

The solution to (8-8sqrt(3)i)^7 is 134217728-134217728sqrt(3)i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (8-8sqrt(3)i)^7

simplify

(8 - 83 i)^{7}

134217728 - 1342177283 i

Solution steps

(8 - 83 i)^{7}

Apply binomial theorem:

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

a = 8, b = - 83 i

= i = 0 \sum 7 (i 7) \cdot 8^{(7 - i)} (- 83 i)^{i}

Expand summation

= \frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 8^{7} (- 83 i)^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 8^{6} (- 83 i)^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 8^{5} (- 83 i)^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 8^{4} (- 83 i)^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 8^{3} (- 83 i)^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 8^{2} (- 83 i)^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 8^{1} (- 83 i)^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 8^{0} (- 83 i)^{7}

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 8^{7} (- 83 i)^{0} : 2097152

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 8^{6} (- 83 i)^{1} : - 146800643 i

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 8^{5} (- 83 i)^{2} : 132120576 i^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 8^{4} (- 83 i)^{3} : - 2202009603 i^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 8^{3} (- 83 i)^{4} : 660602880 i^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 8^{2} (- 83 i)^{5} : - 3963617283 i^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 8^{1} (- 83 i)^{6} : 396361728 i^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 8^{0} (- 83 i)^{7} : - 566231043 i^{7}

= 2097152 - 146800643 i + 132120576 i^{2} - 2202009603 i^{3} + 660602880 i^{4} - 3963617283 i^{5} + 396361728 i^{6} - 566231043 i^{7}

Simplify

2097152 - 146800643 i + 132120576 i^{2} - 2202009603 i^{3} + 660602880 i^{4} - 3963617283 i^{5} + 396361728 i^{6} - 566231043 i^{7} : - 1342177283 i + 134217728

= - 1342177283 i + 134217728

Rewrite in standard complex form:

134217728 - 1342177283 i

= 134217728 - 1342177283 i

\frac{16}{x ^{2} \times ( x - 4 )}

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

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

e \cdot (- \frac{1}{x} + 1)

\frac{( x + 8 )}{( 4 - 3 x ) ^{\frac{1}{2}}}

What is (8-8sqrt(3)i)^7 ?
The solution to (8-8sqrt(3)i)^7 is 134217728-134217728sqrt(3)i