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What is the product of 3√3cis(π/8) and 3√5cis(2π/3)?

 

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 May 6, 2021
 #1
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Used wolfram for the last part :P.

 

cis(pi/8) = sqrt(2 + sqrt(2))/2 + 1/2 i sqrt(2 - sqrt(2))

cis(pi/3) = -1/2 + (i sqrt(3))/2

3 \sqrt{3 * sqrt(2 + sqrt(2))/2 + 1/2 i sqrt(2 - sqrt(2))} * 3 \sqrt{5 * (-1/2 + (i sqrt(3))/2)} = 9 sqrt(5 (-1/2 + (i sqrt(3))/2)) sqrt((3 sqrt(2 + sqrt(2)))/2 + 1/2 i sqrt(2 - sqrt(2)))

 

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