What is ((sqrt(3)+i)^{10})/(1+i) ?

The solution to ((sqrt(3)+i)^{10})/(1+i) is (-256sqrt(3)+256)-256(1+sqrt(3))i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((sqrt(3)+i)^{10})/(1+i)

simplify

\frac{( 3 + i ) ^{10}}{1 + i}

(- 2563 + 256) - 256 (1 + 3) i

Solution steps

\frac{( 3 + i ) ^{10}}{1 + i}

Multiply by the conjugate

\frac{1 - i}{1 - i}

= \frac{( 3 + i ) ^{10} ( 1 - i )}{( 1 + i ) ( 1 - i )}

Simplify

\frac{( 3 + i ) ^{10} ( 1 - i )}{( 1 + i ) ( 1 - i )} : \frac{- 512 i ( 1 + 3 ) - 512 3 + 512}{2}

= \frac{- 512 i ( 1 + 3 ) - 512 3 + 512}{2}

Rewrite

- 512 i (1 + 3) - 5123 + 512

in standard complex form:

(- 5123 + 512) - 512 (1 + 3) i

= \frac{( - 512 3 + 512 ) - 512 ( 1 + 3 ) i}{2}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{- 512 3 + 512}{2} + \frac{- 512 ( 1 + 3 )}{2} i

Simplify

\frac{- 512 3 + 512}{2} + \frac{- 512 ( 1 + 3 )}{2} i : (- 2563 + 256) + (- 256 - 2563) i

= (- 2563 + 256) + (- 256 - 2563) i

Simplify

(- 2563 + 256) + (- 256 - 2563) i : - 2563 + 256 - 256 i (1 + 3)

= - 2563 + 256 - 256 i (1 + 3)

Rewrite in standard complex form:

(- 2563 + 256) - 256 (1 + 3) i

= (- 2563 + 256) - 256 (1 + 3) i

\frac{5 !}{4 ! 1 !}

\frac{1}{12} + \frac{2}{9}

x^{2} > 4 (x + 8)

5 x^{2} + 10 x + 500

u^{4} x^{4} - 81 u^{4}

What is ((sqrt(3)+i)^{10})/(1+i) ?
The solution to ((sqrt(3)+i)^{10})/(1+i) is (-256sqrt(3)+256)-256(1+sqrt(3))i