What is 2(sqrt(3)+i)^7 ?

The solution to 2(sqrt(3)+i)^7 is -128sqrt(3)-128i

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simplify 2(sqrt(3)+i)^7

simplify

2 (3 + i)^{7}

- 1283 - 128 i

Solution steps

2 (3 + i)^{7}

Expand

(3 + i)^{7} : 273 + 189 i + 1893 i^{2} + 315 i^{3} + 1053 i^{4} + 63 i^{5} + 73 i^{6} + i^{7}

= 2 (273 + 189 i + 1893 i^{2} + 315 i^{3} + 1053 i^{4} + 63 i^{5} + 73 i^{6} + i^{7})

Distribute parentheses

= 2 \cdot 273 + 2 \cdot 189 i + 2 \cdot 1893 i^{2} + 2 \cdot 315 i^{3} + 2 \cdot 1053 i^{4} + 2 \cdot 63 i^{5} + 2 \cdot 73 i^{6} + 2 i^{7}

Simplify

2 \cdot 273 + 2 \cdot 189 i + 2 \cdot 1893 i^{2} + 2 \cdot 315 i^{3} + 2 \cdot 1053 i^{4} + 2 \cdot 63 i^{5} + 2 \cdot 73 i^{6} + 2 i^{7} : - 128 i - 1283

= - 128 i - 1283

Rewrite in standard complex form:

- 1283 - 128 i

= - 1283 - 128 i

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