What is expand ((-4-i)^7)/((2-3i)^5) ?

The solution to expand ((-4-i)^7)/((2-3i)^5) is -11613283/371293-(4181810i)/(371293)

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expand ((-4-i)^7)/((2-3i)^5)

expand

\frac{( - 4 - i ) ^{7}}{( 2 - 3 i ) ^{5}}

- \frac{11613283}{371293} - \frac{4181810 i}{371293}

Solution steps

\frac{( - 4 - i ) ^{7}}{( 2 - 3 i ) ^{5}}

(2 - 3 i)^{5} = 122 + 597 i

= \frac{( - 4 - i ) ^{7}}{122 + 597 i}

(- 4 - i)^{7} = 2908 - 20047 i

= \frac{2908 - 20047 i}{122 + 597 i}

Apply complex arithmetic rule:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = 2908, b = - 20047, c = 122, d = 597

= \frac{( 2908 \cdot 122 + ( - 20047 ) \cdot 597 ) + ( - 20047 \cdot 122 - 2908 \cdot 597 ) i}{12 2 ^{2} + 59 7 ^{2}}

Refine

= \frac{- 11613283 - 4181810 i}{371293}

Apply the fraction rule:

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

\frac{- 11613283 - 4181810 i}{371293} = - \frac{11613283}{371293} - \frac{4181810 i}{371293}

= - \frac{11613283}{371293} - \frac{4181810 i}{371293}

\frac{1}{( 1 - n ) ^{2}}

(\frac{2 x}{n})^{2}

- \frac{9 ( y ^{2} + 9 x ^{2} )}{y ^{3}}

x (1 - lo g_{10} (5))

(2 x - 1) e^{2}

What is expand ((-4-i)^7)/((2-3i)^5) ?
The solution to expand ((-4-i)^7)/((2-3i)^5) is -11613283/371293-(4181810i)/(371293)