en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (-5+5i)^5

Solution

simplify

(- 5 + 5 i)^{5}

Solution

12500 - 12500 i

Solution steps

(- 5 + 5 i)^{5}

Apply binomial theorem:

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

a = - 5, b = 5 i

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (- 5)^{5} (5 i)^{0} : - 3125

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (- 5)^{4} (5 i)^{1} : 15625 i

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (- 5)^{3} (5 i)^{2} : - 31250 i^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (- 5)^{2} (5 i)^{3} : 31250 i^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (- 5)^{1} (5 i)^{4} : - 15625 i^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (- 5)^{0} (5 i)^{5} : 3125 i^{5}

= - 3125 + 15625 i - 31250 i^{2} + 31250 i^{3} - 15625 i^{4} + 3125 i^{5}

Simplify

- 3125 + 15625 i - 31250 i^{2} + 31250 i^{3} - 15625 i^{4} + 3125 i^{5} : - 12500 i + 12500

= - 12500 i + 12500

Rewrite in standard complex form:

12500 - 12500 i

= 12500 - 12500 i

Popular Examples

simplify 3*(4-x/9)simplify

3 \cdot (4 - \frac{x}{9})

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

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

expand-1+(-2)(x-(3pi)/4)expand

- 1 + (- 2) (x - \frac{3 π}{4})

expand (1-r)/((x-r)(x-1))expand

\frac{1 - r}{( x - r ) ( x - 1 )}

expand (2(1+sqrt(21)))/5 expand

\frac{2 ( 1 + 21 )}{5}

Frequently Asked Questions (FAQ)

What is (-5+5i)^5 ?
The solution to (-5+5i)^5 is 12500-12500i