What is ((3-3i)(-2+2sqrt(3)i))^{10} ?

The solution to ((3-3i)(-2+2sqrt(3)i))^{10} is ((-6+6sqrt(3))+6(sqrt(3)+1)i)^{10}

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simplify ((3-3i)(-2+2sqrt(3)i))^{10}

simplify

((3 - 3 i) (- 2 + 23 i))^{10}

((- 6 + 63) + 6 (3 + 1) i)^{10}

Solution steps

((3 - 3 i) (- 2 + 23 i))^{10}

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

(3 - 3 i) (- 2 + 23 i) = (3 (- 2) - (- 3) \cdot 23) + (3 \cdot 23 - 3 (- 2)) i

= ((3 (- 2) - (- 3) \cdot 23) + (3 \cdot 23 - 3 (- 2)) i)^{10}

Simplify

(3 (- 2) - (- 3) \cdot 23) + (3 \cdot 23 - 3 (- 2)) i : (- 6 + 63) + (63 + 6) i

= ((- 6 + 63) + (63 + 6) i)^{10}

Apply rule:

(a) = a

(- 6 + 63) = - 6 + 63

= (- 6 + 63 + (63 + 6) i)^{10}

= (- 6 + 63 + i (63 + 6))^{10}

Expand

i (63 + 6) : 6 i (3 + 1)

= (- 6 + 63 + 6 i (3 + 1))^{10}

Rewrite in standard complex form:

((- 6 + 63) + 6 (3 + 1) i)^{10}

= ((- 6 + 63) + 6 (3 + 1) i)^{10}

\frac{3}{8} - \frac{6}{48}

(7 x - 1) - (2 x^{2} + 4 x + 7)

\frac{7}{8} \div \frac{21}{16}

2 (6 + 12)

(x - 5) (4 x^{2} - 2 x + 1)

What is ((3-3i)(-2+2sqrt(3)i))^{10} ?
The solution to ((3-3i)(-2+2sqrt(3)i))^{10} is ((-6+6sqrt(3))+6(sqrt(3)+1)i)^{10}