en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (2+i)^4

Solution

expand

(2 + i)^{4}

Solution

- 7 + 24 i

Solution steps

(2 + i)^{4}

Apply binomial theorem:

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

a = 2, b = i

= i = 0 \sum 4 (i 4) \cdot 2^{(4 - i)} i^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 2^{4} i^{0} : 16

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 2^{3} i^{1} : 32 i

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 2^{2} i^{2} : 24 i^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 2^{1} i^{3} : 8 i^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 2^{0} i^{4} : i^{4}

= 16 + 32 i + 24 i^{2} + 8 i^{3} + i^{4}

Simplify

16 + 32 i + 24 i^{2} + 8 i^{3} + i^{4} : 24 i - 7

= 24 i - 7

Rewrite in standard complex form:

- 7 + 24 i

= - 7 + 24 i

Popular Examples

expand (2+i)^3 expand

(2 + i)^{3}

(d^2)/(dx^2)((y)(2xe^{x^2}-2))

\frac{d ^{2}}{d x ^{2}} ((y) (2 x e^{x^{2}} - 2))

expand x^{3/2}*(2x^2+x-1)expand

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

expand (2+sqrt(x))(3-sqrt(3))expand

(2 + x) (3 - 3)

expand ((x+7)(x-2))/(2(x^2-3))expand

\frac{( x + 7 ) ( x - 2 )}{2 ( x ^{2} - 3 )}

Frequently Asked Questions (FAQ)

What is expand (2+i)^4 ?
The solution to expand (2+i)^4 is -7+24i