en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (-2-i)^4

Solution

simplify

(- 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) (- 2)^{(4 - i)} (- i)^{i}

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (- 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 r^2(cos^2(θ)-sin^2(θ))expand

r^{2} (cos^{2} (θ) - sin^{2} (θ))

simplify (t+t^2i)^2 simplify

(t + t^{2} i)^{2}

expand (2xy+4x^3y^2)dx+(3x^2+4x^4y)dy expand

(2 x y + 4 x^{3} y^{2}) d x + (3 x^{2} + 4 x^{4} y) d y

expand (x^2-81)y''(x)+(9-x)y'(x)+(x^2+18x+81)y expand

(x^{2} - 81) y^{''} (x) + (9 - x) y^{'} (x) + (x^{2} + 18 x + 81) y

simplify (sqrt(3)+i)^{10}simplify

(3 + i)^{10}

Frequently Asked Questions (FAQ)

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