Simplify (sqrt(3)+i)^8 and write in the form a + bi

popljuvao69

popljuvao69

Answered question

2022-08-12

Simplify (\sqrt{3}+i)^8 and write in the form a + bi

Answer & Explanation

Jewel Brooks

Jewel Brooks

Beginner2022-08-13Added 15 answers

3 + i = 2 ( 3 2 + 1 2 i ) = 2 ( cos π 6 + i sin π 6 ) ( 3 + i ) 8 = [ 2 ( cos π 6 + i sin π 6 ) ] 8 = 2 8 [ cos 8 π 6 + i sin 8 π 6 ] = 256 [ cos 4 π 3 + i sin 4 π 3 ] = 256 [ 1 2 3 2 i ] = 128 128 3 i

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