What is expand-((4-4i)^{15})/(125000) ?

The solution to expand-((4-4i)^{15})/(125000) is -17179869184/15625-i(4^{15}*16)/(15625)

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expand-((4-4i)^{15})/(125000)

expand

- \frac{( 4 - 4 i ) ^{15}}{125000}

- \frac{17179869184}{15625} - i \frac{4 ^{15} \cdot 16}{15625}

Solution steps

- \frac{( 4 - 4 i ) ^{15}}{125000}

(4 - 4 i)^{15} = 4^{15} \cdot 128 i + 4^{15} \cdot 143 - 16106127360

= - \frac{4 ^{15} \cdot 128 i + 4 ^{15} \cdot 143 - 16106127360}{125000}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{4 ^{15} \cdot 128 i + 4 ^{15} \cdot 143 - 16106127360}{125000} = - (\frac{4 ^{15} \cdot 128 i}{125000}) - (\frac{4 ^{15} \cdot 143}{125000}) - (- \frac{16106127360}{125000})

= - (\frac{4 ^{15} \cdot 128 i}{125000}) - (\frac{4 ^{15} \cdot 143}{125000}) - (- \frac{16106127360}{125000})

Remove parentheses:

(a) = a, - (- a) = a

= - \frac{4 ^{15} \cdot 128 i}{125000} - \frac{4 ^{15} \cdot 143}{125000} + \frac{16106127360}{125000}

\frac{4 ^{15} \cdot 128 i}{125000} = \frac{4 ^{15} \cdot 16 i}{15625}

\frac{4 ^{15} \cdot 143}{125000} = \frac{19193135104}{15625}

\frac{16106127360}{125000} = \frac{402653184}{3125}

= - \frac{4 ^{15} \cdot 16 i}{15625} - \frac{19193135104}{15625} + \frac{402653184}{3125}

Rewrite

- \frac{4 ^{15} \cdot 16 i}{15625} - \frac{19193135104}{15625} + \frac{402653184}{3125}

in standard complex form:

- \frac{17179869184}{15625} - \frac{4 ^{15} \cdot 16}{15625} i

= - \frac{17179869184}{15625} - \frac{4 ^{15} \cdot 16}{15625} i

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

\frac{q ( L - x ) \cdot ( L + 2 x )}{6}

(x y + 1) d x + x (x + 4 y - 2) d y

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\frac{2 ( - 2 f ^{2} + 1 )}{f ^{3}}

What is expand-((4-4i)^{15})/(125000) ?
The solution to expand-((4-4i)^{15})/(125000) is -17179869184/15625-i(4^{15}*16)/(15625)