en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (-1-i)^4

Solution

simplify

(- 1 - i)^{4}

Solution

- 4

Solution steps

(- 1 - i)^{4}

Apply binomial theorem:

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

a = - 1, b = - i

= i = 0 \sum 4 (i 4) (- 1)^{(4 - i)} (- i)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (- 1)^{4} (- i)^{0} : 1

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (- 1)^{2} (- i)^{2} : 6 i^{2}

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (- 1)^{0} (- i)^{4} : i^{4}

= 1 + 4 i + 6 i^{2} + 4 i^{3} + i^{4}

Simplify

1 + 4 i + 6 i^{2} + 4 i^{3} + i^{4} : - 4

= - 4

Popular Examples

simplify-3/4-4 simplify

- \frac{3}{4} - 4

factor 5x^{3/2}-15x^{1/2}+10x^{-1/2}factor

5 x^{\frac{3}{2}} - 15 x^{\frac{1}{2}} + 10 x^{- \frac{1}{2}}

- 7 x - 8 = - 16

factor xy^5+x^3y^3 factor

x y^{5} + x^{3} y^{3}

x^{2} - 12 x = - 32

Frequently Asked Questions (FAQ)

What is (-1-i)^4 ?
The solution to (-1-i)^4 is -4