What is expand ((1+i)^5)/((2+3i)^5) ?

The solution to expand ((1+i)^5)/((2+3i)^5) is 1900/371293-(2876i)/(371293)

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expand ((1+i)^5)/((2+3i)^5)

expand

\frac{( 1 + i ) ^{5}}{( 2 + 3 i ) ^{5}}

\frac{1900}{371293} - \frac{2876 i}{371293}

Solution steps

\frac{( 1 + i ) ^{5}}{( 2 + 3 i ) ^{5}}

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

= \frac{( 1 + i ) ^{5}}{122 - 597 i}

(1 + i)^{5} = - 4 - 4 i

= \frac{( - 4 - 4 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 = - 4, b = - 4, c = 122, d = - 597

= \frac{( - 4 \cdot 122 + ( - 4 ) ( - 597 ) ) + ( - 4 \cdot 122 - ( - 4 ) ( - 597 ) ) i}{12 2 ^{2} + ( - 597 ) ^{2}}

Refine

= \frac{1900 - 2876 i}{371293}

Apply the fraction rule:

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

\frac{1900 - 2876 i}{371293} = \frac{1900}{371293} - \frac{2876 i}{371293}

= \frac{1900}{371293} - \frac{2876 i}{371293}

\frac{d}{d y} ((x) (1 - x e^{- x}))

(x, y) \Rightarrow (x - 5, y - 3)

arcsin (- 8 (x + c))

\frac{8 ( 3 x - 7 )}{5}

13 \cdot (30 - \frac{60}{π})

What is expand ((1+i)^5)/((2+3i)^5) ?
The solution to expand ((1+i)^5)/((2+3i)^5) is 1900/371293-(2876i)/(371293)