What is (2sqrt(3)-2i)^5 ?

The solution to (2sqrt(3)-2i)^5 is -512sqrt(3)-512i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (2sqrt(3)-2i)^5

simplify

(23 - 2 i)^{5}

- 5123 - 512 i

Solution steps

(23 - 2 i)^{5}

Apply binomial theorem:

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

a = 23, b = - 2 i

= i = 0 \sum 5 (i 5) (23)^{(5 - i)} (- 2 i)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (23)^{5} (- 2 i)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (23)^{4} (- 2 i)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (23)^{3} (- 2 i)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (23)^{2} (- 2 i)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (23)^{1} (- 2 i)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (23)^{0} (- 2 i)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (23)^{5} (- 2 i)^{0} : 2883

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (23)^{4} (- 2 i)^{1} : - 1440 i

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (23)^{3} (- 2 i)^{2} : 9603 i^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (23)^{2} (- 2 i)^{3} : - 960 i^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (23)^{1} (- 2 i)^{4} : 1603 i^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (23)^{0} (- 2 i)^{5} : - 32 i^{5}

= 2883 - 1440 i + 9603 i^{2} - 960 i^{3} + 1603 i^{4} - 32 i^{5}

Simplify

2883 - 1440 i + 9603 i^{2} - 960 i^{3} + 1603 i^{4} - 32 i^{5} : - 512 i - 5123

= - 512 i - 5123

Rewrite in standard complex form:

- 5123 - 512 i

= - 5123 - 512 i

(- 1 - 2 i)^{2}

f (x, y) (x^{2} - 3 x y + x - y^{2} + 4) - λ (x + y - 2)

(e^{t} - t)^{2}

2 (2^{\frac{n}{2}} - 1)

(1 - 2 z i)^{2}