What is (sqrt(3)-sqrt(2)i)^6 ?

The solution to (sqrt(3)-sqrt(2)i)^6 is -71+42sqrt(6)i

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simplify (sqrt(3)-sqrt(2)i)^6

simplify

(3 - 2 i)^{6}

- 71 + 426 i

Solution steps

(3 - 2 i)^{6}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 3, b = - 2 i

= i = 0 \sum 6 (i 6) (3)^{(6 - i)} (- 2 i)^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} (3)^{6} (- 2 i)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (3)^{5} (- 2 i)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (3)^{4} (- 2 i)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (3)^{3} (- 2 i)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (3)^{2} (- 2 i)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (3)^{1} (- 2 i)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (3)^{0} (- 2 i)^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (3)^{6} (- 2 i)^{0} : 27

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (3)^{5} (- 2 i)^{1} : - 546 i

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (3)^{4} (- 2 i)^{2} : 270 i^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (3)^{3} (- 2 i)^{3} : - 1206 i^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (3)^{2} (- 2 i)^{4} : 180 i^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (3)^{1} (- 2 i)^{5} : - 246 i^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (3)^{0} (- 2 i)^{6} : 8 i^{6}

= 27 - 546 i + 270 i^{2} - 1206 i^{3} + 180 i^{4} - 246 i^{5} + 8 i^{6}

Simplify

27 - 546 i + 270 i^{2} - 1206 i^{3} + 180 i^{4} - 246 i^{5} + 8 i^{6} : 426 i - 71

= 426 i - 71

Rewrite in standard complex form:

- 71 + 426 i

= - 71 + 426 i

\frac{\partial}{\partial t} ((x) (s + t))

(1 + x) d y

(x + i y)^{4}

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

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

What is (sqrt(3)-sqrt(2)i)^6 ?
The solution to (sqrt(3)-sqrt(2)i)^6 is -71+42sqrt(6)i