What is expand 1000(1+i/(12))^{12} ?

The solution to expand 1000(1+i/(12))^{12} is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand 1000(1+i/(12))^{12}

expand

1000 (1 + \frac{i}{12})^{12}

\frac{1625 + 3000 i}{3} + (\frac{6875}{288} - \frac{9625}{31104} + \frac{6875}{5971968} - \frac{1375}{1289945088} + \frac{125}{1114512556032}) + (- \frac{6875}{54} + \frac{1375}{432} - \frac{1375}{62208} + \frac{6875}{161243136} - \frac{125}{2 ^{17} \cdot 59049}) i

Solution steps

1000 (1 + \frac{i}{12})^{12}

Expand

(1 + \frac{i}{12})^{12} : 1 + i + \frac{11 i ^{2}}{24} + \frac{55 i ^{3}}{432} + \frac{55 i ^{4}}{2304} + \frac{11 i ^{5}}{3456} + \frac{77 i ^{6}}{248832} + \frac{11 i ^{7}}{497664} + \frac{55 i ^{8}}{47775744} + \frac{55 i ^{9}}{1289945088} + \frac{11 i ^{10}}{10319560704} + \frac{i ^{11}}{1 2 ^{10}} + \frac{i ^{12}}{1 2 ^{12}}

= 1000 (1 + i + \frac{11 i ^{2}}{24} + \frac{55 i ^{3}}{432} + \frac{55 i ^{4}}{2304} + \frac{11 i ^{5}}{3456} + \frac{77 i ^{6}}{248832} + \frac{11 i ^{7}}{497664} + \frac{55 i ^{8}}{47775744} + \frac{55 i ^{9}}{1289945088} + \frac{11 i ^{10}}{10319560704} + \frac{i ^{11}}{1 2 ^{10}} + \frac{i ^{12}}{1 2 ^{12}})

Distribute parentheses

= 1000 \cdot 1 + 1000 i + 1000 \cdot \frac{11 i ^{2}}{24} + 1000 \cdot \frac{55 i ^{3}}{432} + 1000 \cdot \frac{55 i ^{4}}{2304} + 1000 \cdot \frac{11 i ^{5}}{3456} + 1000 \cdot \frac{77 i ^{6}}{248832} + 1000 \cdot \frac{11 i ^{7}}{497664} + 1000 \cdot \frac{55 i ^{8}}{47775744} + 1000 \cdot \frac{55 i ^{9}}{1289945088} + 1000 \cdot \frac{11 i ^{10}}{10319560704} + 1000 \cdot \frac{i ^{11}}{1 2 ^{10}} + 1000 \cdot \frac{i ^{12}}{1 2 ^{12}}

Simplify

1000 \cdot 1 + 1000 i + 1000 \cdot \frac{11 i ^{2}}{24} + 1000 \cdot \frac{55 i ^{3}}{432} + 1000 \cdot \frac{55 i ^{4}}{2304} + 1000 \cdot \frac{11 i ^{5}}{3456} + 1000 \cdot \frac{77 i ^{6}}{248832} + 1000 \cdot \frac{11 i ^{7}}{497664} + 1000 \cdot \frac{55 i ^{8}}{47775744} + 1000 \cdot \frac{55 i ^{9}}{1289945088} + 1000 \cdot \frac{11 i ^{10}}{10319560704} + 1000 \cdot \frac{i ^{11}}{1 2 ^{10}} + 1000 \cdot \frac{i ^{12}}{1 2 ^{12}} : \frac{3000 i + 1625}{3} - \frac{6875 i}{54} + \frac{6875}{288} + \frac{1375 i}{432} - \frac{9625}{31104} - \frac{1375 i}{62208} + \frac{6875}{5971968} + \frac{6875 i}{161243136} - \frac{1375}{1289945088} - \frac{125 i}{2 ^{17} \cdot 59049} + \frac{125}{1114512556032}

= \frac{3000 i + 1625}{3} - \frac{6875 i}{54} + \frac{6875}{288} + \frac{1375 i}{432} - \frac{9625}{31104} - \frac{1375 i}{62208} + \frac{6875}{5971968} + \frac{6875 i}{161243136} - \frac{1375}{1289945088} - \frac{125 i}{2 ^{17} \cdot 59049} + \frac{125}{1114512556032}

Rewrite in standard complex form:

\frac{1625 + 3000 i}{3} + (\frac{6875}{288} - \frac{9625}{31104} + \frac{6875}{5971968} - \frac{1375}{1289945088} + \frac{125}{1114512556032}) + (- \frac{6875}{54} + \frac{1375}{432} - \frac{1375}{62208} + \frac{6875}{161243136} - \frac{125}{2 ^{17} \cdot 59049}) i

= \frac{1625 + 3000 i}{3} + (\frac{6875}{288} - \frac{9625}{31104} + \frac{6875}{5971968} - \frac{1375}{1289945088} + \frac{125}{1114512556032}) + (- \frac{6875}{54} + \frac{1375}{432} - \frac{1375}{62208} + \frac{6875}{161243136} - \frac{125}{2 ^{17} \cdot 59049}) i

ln (x) (\frac{x ^{3}}{3} + 3 x) - \frac{1}{3} (\frac{x ^{3}}{3} + 9 x) + c

(1 - 3 i)^{16}

lo g_{10} (x^{7} y^{- 4})

(b - x + ((x + b) \cdot (5 \cdot b - 3 \cdot x)))^{2}

(x - 2) (x + 6) (x - \frac{1}{2})

What is expand 1000(1+i/(12))^{12} ?
The solution to expand 1000(1+i/(12))^{12} is