en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (4-i)^6

Solution

simplify

(4 - i)^{6}

Solution

495 - 4888 i

Solution steps

(4 - i)^{6}

Apply binomial theorem:

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

a = 4, b = - i

= i = 0 \sum 6 (i 6) \cdot 4^{(6 - i)} (- i)^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 4^{6} (- i)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 4^{5} (- i)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 4^{4} (- i)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 4^{3} (- i)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 4^{2} (- i)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 4^{1} (- i)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 4^{0} (- i)^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 4^{6} (- i)^{0} : 4096

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 4^{5} (- i)^{1} : - 6144 i

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 4^{4} (- i)^{2} : 3840 i^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 4^{3} (- i)^{3} : - 1280 i^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 4^{2} (- i)^{4} : 240 i^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 4^{1} (- i)^{5} : - 24 i^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 4^{0} (- i)^{6} : i^{6}

= 4096 - 6144 i + 3840 i^{2} - 1280 i^{3} + 240 i^{4} - 24 i^{5} + i^{6}

Simplify

4096 - 6144 i + 3840 i^{2} - 1280 i^{3} + 240 i^{4} - 24 i^{5} + i^{6} : - 4888 i + 495

= - 4888 i + 495

Rewrite in standard complex form:

495 - 4888 i

= 495 - 4888 i

Popular Examples

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

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

expand (4pi)/((w-pi)^2)expand

\frac{4 π}{( w - π ) ^{2}}

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

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

expand (32768x^7(2x^8-1))/(2x-1)expand

\frac{32768 x ^{7} ( 2 x ^{8} - 1 )}{2 x - 1}

expand sqrt((1)^2+(2t)^2+(3t^2)^2)expand

(1)^{2} + (2 t)^{2} + (3 t^{2})^{2}

Frequently Asked Questions (FAQ)

What is (4-i)^6 ?
The solution to (4-i)^6 is 495-4888i