en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (-1+2i)^4

Solution

simplify

(- 1 + 2 i)^{4}

Solution

- 7 + 24 i

Solution steps

(- 1 + 2 i)^{4}

Apply binomial theorem:

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

a = - 1, b = 2 i

= i = 0 \sum 4 (i 4) (- 1)^{(4 - i)} (2 i)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (- 1)^{4} (2 i)^{0} : 1

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (- 1)^{2} (2 i)^{2} : 24 i^{2}

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (- 1)^{0} (2 i)^{4} : 16 i^{4}

= 1 - 8 i + 24 i^{2} - 32 i^{3} + 16 i^{4}

Simplify

1 - 8 i + 24 i^{2} - 32 i^{3} + 16 i^{4} : 24 i - 7

= 24 i - 7

Rewrite in standard complex form:

- 7 + 24 i

= - 7 + 24 i

Popular Examples

simplify (3+i)^4 simplify

(3 + i)^{4}

expand (3x+2y=2,)(x-y=9)expand

(3 x + 2 y = 2,) (x - y = 9)

simplify (sqrt(x)+sqrt(3))^2 simplify

(x + 3)^{2}

expand (e^t+e^{2t})^2 expand

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

expand 1/((x+1)^2)expand

\frac{1}{( x + 1 ) ^{2}}

Frequently Asked Questions (FAQ)

What is (-1+2i)^4 ?
The solution to (-1+2i)^4 is -7+24i