en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (-2+2i)^4

Solution

simplify

(- 2 + 2 i)^{4}

Solution

- 64

Solution steps

(- 2 + 2 i)^{4}

Apply binomial theorem:

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

a = - 2, b = 2 i

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (- 2)^{3} (2 i)^{1} : - 64 i

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (- 2)^{2} (2 i)^{2} : 96 i^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (- 2)^{1} (2 i)^{3} : - 64 i^{3}

Simplify

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

= 16 - 64 i + 96 i^{2} - 64 i^{3} + 16 i^{4}

Simplify

16 - 64 i + 96 i^{2} - 64 i^{3} + 16 i^{4} : - 64

= - 64

Popular Examples

simplify sqrt(4sin^2(t)+4cos^2(t))simplify

4 sin^{2} (t) + 4 cos^{2} (t)

simplify \lfloor-0.1\rfloor simplify

⌊ - 0.1 ⌋

simplify 1+4x-5x+8+x-9 simplify

1 + 4 x - 5 x + 8 + x - 9

simplify (a^8)/(a^3)simplify

\frac{a ^{8}}{a ^{3}}

simplify t*t simplify

t \cdot t

Frequently Asked Questions (FAQ)

What is (-2+2i)^4 ?
The solution to (-2+2i)^4 is -64