en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (5-4i)^4

Solution

simplify

(5 - 4 i)^{4}

Solution

- 1519 - 720 i

Solution steps

(5 - 4 i)^{4}

Apply binomial theorem:

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

a = 5, b = - 4 i

= i = 0 \sum 4 (i 4) \cdot 5^{(4 - i)} (- 4 i)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 5^{4} (- 4 i)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 5^{3} (- 4 i)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 5^{2} (- 4 i)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 5^{1} (- 4 i)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 5^{0} (- 4 i)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 5^{4} (- 4 i)^{0} : 625

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 5^{3} (- 4 i)^{1} : - 2000 i

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 5^{2} (- 4 i)^{2} : 2400 i^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 5^{1} (- 4 i)^{3} : - 1280 i^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 5^{0} (- 4 i)^{4} : 256 i^{4}

= 625 - 2000 i + 2400 i^{2} - 1280 i^{3} + 256 i^{4}

Simplify

625 - 2000 i + 2400 i^{2} - 1280 i^{3} + 256 i^{4} : - 720 i - 1519

= - 720 i - 1519

Rewrite in standard complex form:

- 1519 - 720 i

= - 1519 - 720 i

Popular Examples

expand (1/4+1/(2^{k+1)})(1-1/(2^{k+1)})expand

(\frac{1}{4} + \frac{1}{2 ^{k + 1}}) (1 - \frac{1}{2 ^{k + 1}})

simplify (x+2sqrt(5))(x-2sqrt(5))simplify

(x + 25) (x - 25)

expand (f(x+h)-f(x))/h expand

\frac{f ( x + h ) - f ( x )}{h}

simplify (5z+3i)^2 simplify

(5 z + 3 i)^{2}

expand ((e^x-e^{-x})/2)^2 expand

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

Frequently Asked Questions (FAQ)

What is (5-4i)^4 ?
The solution to (5-4i)^4 is -1519-720i