What is expand ((sqrt(2)+i)^9)/((1-sqrt(2)i)^8) ?

The solution to expand ((sqrt(2)+i)^9)/((1-sqrt(2)i)^8) is sqrt(2)+i

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expand ((sqrt(2)+i)^9)/((1-sqrt(2)i)^8)

expand

\frac{( 2 + i ) ^{9}}{( 1 - 2 i ) ^{8}}

2 + i

Solution steps

\frac{( 2 + i ) ^{9}}{( 1 - 2 i ) ^{8}}

(1 - 2 i)^{8} = 17 - 562 i

= \frac{( 2 + i ) ^{9}}{17 - 56 2 i}

(2 + i)^{9} = - 95 i + 732

= \frac{( - 95 i + 73 2 )}{17 - 56 2 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 = 732, b = - 95, c = 17, d = - 562

= \frac{( 73 2 \cdot 17 + ( - 95 ) ( - 56 2 ) ) + ( - 95 \cdot 17 - 73 2 ( - 56 2 ) ) i}{1 7 ^{2} + ( - 56 2 ) ^{2}}

Refine

= \frac{6561 2 + 6561 i}{6561}

Simplify

\frac{6561 2 + 6561 i}{6561} : 2 + i

= 2 + i

(x^{2} - x + 1) (e^{x})

\frac{3 x ^{2} + 10 x + 3}{( x + 1 ) ^{2} ( x + 2 ) ( x ^{2} + 1 )}

(5 x + 16 + 4)^{2}

\frac{1}{2} (0.5 \cdot 20 + 1) + \frac{1}{2} (0.5 \cdot 5 + 1)

A (- 1, 0) B (2, - 8)

What is expand ((sqrt(2)+i)^9)/((1-sqrt(2)i)^8) ?
The solution to expand ((sqrt(2)+i)^9)/((1-sqrt(2)i)^8) is sqrt(2)+i