What is expand |((3+4i)^4)/((2-i)^{10)}| ?

The solution to expand |((3+4i)^4)/((2-i)^{10)}| is (sqrt(922077^2+1721764^2))/(9765625)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand |((3+4i)^4)/((2-i)^{10)}|

expand

\frac{( 3 + 4 i ) ^{4}}{( 2 - i ) ^{10}}

\frac{92207 7 ^{2} + 172176 4 ^{2}}{9765625}

Decimal Notation

0.2

Solution steps

\frac{( 3 + 4 i ) ^{4}}{( 2 - i ) ^{10}}

(2 - i)^{10} = - 237 + 3116 i

= \frac{( 3 + 4 i ) ^{4}}{( - 237 + 3116 i )}

(3 + 4 i)^{4} = - 527 - 336 i

= \frac{( - 527 - 336 i )}{( - 237 + 3116 i )}

Remove parentheses:

(- a) = - a

= \frac{- 527 - 336 i}{- 237 + 3116 i}

\frac{- 527 - 336 i}{- 237 + 3116 i} : \frac{- 922077 + 1721764 i}{9765625}

= \frac{- 922077 + 1721764 i}{9765625}

Rewrite

\frac{- 922077 + 1721764 i}{9765625}

- \frac{922077}{9765625} + \frac{1721764}{9765625} i

= - \frac{922077}{9765625} + i \frac{1721764}{9765625}

∣ a + bi ∣ = (a + bi) (a - bi) = a^{2} + b^{2}

With

a = - \frac{922077}{9765625}, b = \frac{1721764}{9765625}

= (- \frac{922077}{9765625})^{2} + (\frac{1721764}{9765625})^{2}

Simplify

= \frac{92207 7 ^{2} + 172176 4 ^{2}}{9765625}

(a + b x + c x^{2}) (d + e x + f x^{2})

sec (x) (csc (x) - 1) + cos (x) (sec^{2} (x) - csc (x))

(23 - 2 i)^{8}

\frac{x + 1}{x ^{\frac{2}{3}} ( x + 3 ) ^{\frac{1}{3}}}

\frac{2 ( x ^{4} - 1 )}{x ^{3}}

What is expand |((3+4i)^4)/((2-i)^{10)}| ?
The solution to expand |((3+4i)^4)/((2-i)^{10)}| is (sqrt(922077^2+1721764^2))/(9765625)